query: Need a formula to determine monthly payments received at time t if I'm reinvesting my returns

positive: How does compounding of annual interest work? answers this question. It's not simple compound interest. It's a time value of money calculation similar to mortgage calculations. Only the cash flow is the other way, a 'deposit' instead of 'payment'. When using a finance calculator such as the TI-BA35 (Note, it's no longer manufactured, but you can find secondhand. It was the first electronic device I ever loved. Seriously) you enter PV (present value) FV (future value) Int (the interest rate) nPer (number of periods) PMT (payment).  For a mortgage, there's a PV, but FV = $0. For you, it's reversed. PMT on this model is a positive number, for you it's negative, the amount you deposit. You also need to account for the fact that a mortgage is paid on day 31, but you start deposits on Day 1. See the other answer (I linked at start) for the equations.

positive: With 10% return over three years, depositing $900 each month, in three years $34,039.30.  Re. downvote. I guess this is too brief and without explanation, but I was rushing.  If you want further explanation of how this is calculated check the link already posted by JoeTaxpayer, and have a look at the formula for continuously compounded return.  Also, try out the numbers in the simplified example below yourself.  E.g.  Addendum mhoran_psprep has pointed out that I didn't read the OP's post closely enough.  With rolling investments the total return will be:  Where n is the month number i.e. 36, 37, etc.

negative: Dividend reinvestment plans are a great option for some of your savings. By making small, regular investments, combined with reinvested dividends, you can accumulate a significant nest egg. Pick a medium to large cap company that looks to be around for the foreseeable future, such as JNJ, 3M, GE, or even Exxon. These companies typically raise their dividends every year or so, and this can be a significant portion of your long term gains. Plus, these programs are usually offered with miniscule fees. Also, have a go at the interest rate formulas contained in your favorite spreadsheet application. Calculate the FutureValue of a series of payments at various interest rates, to see what you can expect. While you cannot depend on earning a specific rate with a stock investment, a basic familiarity with the formula can help you determine a rate of return you should aim for.

negative: What's the present value of using the payment plan? In all common sense the present value of a loan is the value that you can pay in the present to avoid taking a loan, which in this case is the lump sum payment of $2495.  That rather supposes the question is a trick, providing irrelevant information about the stock market. However, if some strange interpretation is required which ignores the lump sum and wants to know how much you need in the present to pay the loan while being able to make 8% on the stock market that can be done. I will initially assume that since the lender's APR works out about 9.6% per month that the 8% from the stock market is also per month, but will also calculate for 8% annual effective and an 8% annual nominal rate. The calculation If you have $x in hand (present value) and it is exactly enough to take the loan while investing in the stock market, the value in successive months is $x plus the market return less the loan payment.  In the third month the loan is paid down so the balance is zero. I.e. So the present value of using the payment plan while investing is $2569.37. You would need $2569.37 to cover the loan while investing, which is more than the $2495 lump sum payment requires.  Therefore, it would be advisable to make the lump sum payment because it is less expensive: If you have $2569.37 in hand it would be best to pay the lump sum and invest the remaining $74.37 in the stock market.  Otherwise you invest $2569.37 (initially), pay the loan and end up with $0 in three months. One might ask, what rate of return would the stock market need to yield to make it worth taking the loan? The APR proposed by the loan can be calculated.   The present value of a loan is equal to the sum of the payments discounted to present value.  I.e. with  ∴ by induction  So by comparing the $2495 lump sum payment with $997 over 3 x monthly instalments the interest rate implied by the loan can be found. Solving for r If you could obtain 9.64431% per month on the stock market the $x cash in hand required would be calculated by This is equal to the lump sum payment, so the calculated interest is comparable to the stock market rate of return.  If you could gain more than 9.64431% per month on the stock market it would be better to invest and take the loan. Recurrence Form Solving the recurrence form shows the calculation is equivalent to the loan formula, e.g. becomes v[m + 1] = (1 + y) v[m] - p where v[0] = pv where In the final month v[final] = 0, i.e. when m = 3 Compare with the earlier loan formula: s = (d - d (1 + r)^-n) / r They are exactly equivalent, which is quite interesting, (because it wasn't immediately obvious to me that what the lender charges is the mirror opposite of what you gain by investing). The present value can be now be calculated using the formula. Still assuming the 8% stock market return is per month. If the stock market yield is 8% per annum effective rate and if it is given as a nominal annual yield, 8% compounded monthly

negative: If you think you can manage the risk and the spread is ultimately worth it to you, there's nothing stopping you. I know in the U.S., in CA specifically, you need to have $85,000 annual income or net worth over some threshold to be able to loan more than $2,500 via peer-to-peer loan investing.  I've had an account at prosper since around 2010, it does pretty well.  It's made my taxes a bit more complicated each year, but it's been profitable for me.  I wouldn't lever up on it though. My Prosper Experience My experience with Prosper has generally been positive.  My real motivation for starting the account was generating a dataset that I could analyze, here's some of that analysis. I started the account by trickling $100 /month in to buy four $25 loans.  Any payments received from these loans were used to buy more $25 loans.  I've kept my risk to an average of about A- (AA, A, B, C, D, E, HR are the grades); though the interest rates have reduced over time.  At this point, I have a few hundred loans outstanding in various stages of completion.  In calendar 2015 I had a monthly average of 0.75% of my loans charged-off and about 3% of loans at some stage of delinquency.   I receive about 5.5% of my principle value in receipts on average each month, including loan pay-offs and charge-offs.  Interest and other non-principle payments comprise just shy of 20% of my monthly receipts.  Prosper's 1% maintenance fee translates to about 8% of my monthly non-principle receipts.  It's all a pretty fine line, it wouldn't take many defaults to turn my annual return negative; though in 5 years it hasn't happened yet.  Considering only monthly charge-offs against monthly non-principle receipts I had two net negative months in 2015.  I made about a net 4.5% annual return on my average monthly outstanding principle for calendar 2015.  When I log in to my Prosper account it claims my return  is closer to 7.5% (I'm not sure how that number is calculated). The key is diversifying your risk just like a bank would.  I don't know how the other services function at a nuts and bolts level.  With prosper I choose which loans to fund which means I determine my risk level.  I assume the other services function similarly.   Regarding collection of charged-off loans.  I don't know how much real effort is expended by Prosper.  I've had a few notes sold for about 10% of the outstanding balance; and I don't know who they were sold to.  Comically, I have loan that's made more payments in collections than when it was in good standing.  There is definitely more to this than handing over $15,000 and receiving 6% on it.

negative: I believe you're looking for some sort of formula that will determine how changes in savings, investing, and spending will affect economic growth.  If such a formula existed (and worked) then central planning would work since a couple of people could pull some levers to encourage more savings, or more investing, or more spending - depending on what was needed at that particular time.  Unfortunately, no magic formula exists and so no person has enough knowledge to determine what the proper amount of savings, investing, or spending should be at a given time. I found this resource particular helpful in describing the interactions between savings, consumption, and investing.

negative: "The short of it is that bonds are valued based on a fundamental concept of finance called the ""time value of money"". Stated simply, $100 one year from now is not the same as $100 now. If you had $100 now, you could use it to make more money and have more than $100 in a year. Conversely, if you didn't invest it, the $100 would not buy as much in a year as it would now, and so it would lose real value. Therefore, for these two benefits to be worth the same, the money received a year from now must be more than $100, in the amount of what you could make with $100 if you had it now, or at least the rate of inflation. Or, the amount received now could be less than the amount recieved a year from now, such that if you invested this lesser amount you'd expect to have $100 in a year. The simplest bonds simply pay their face value at maturity, and are sold for less than their face value, the difference being the cost to borrow the cash; ""interest"". These are called ""zero-coupon bonds"" and they're around, if maybe uncommon. The price people will pay for these bonds is their ""present value"", and the difference between the present value and face value determines a ""yield""; a rate of return, similar to the interest rate on a CD. Now, zero-coupon bonds are uncommon because they cost a lot. If I buy a zero-coupon bond, I'm basically tying up my money until maturity; I see nothing until the full bond is paid. As such, I would expect the bond issuer to sell me the bond at a rate that makes it worth my while to keep the money tied up. So basically, the bond issuer is paying me compound interest on the loan. The future value of an investment now at a given rate is given by FV = PV(1+r)t. To gain $1 million in new cash today, and pay a 5% yield over 10 years, a company or municipality would have to issue $1.629 million in bonds. You see the effects of the compounding there; the company is paying 5% a year on the principal each year, plus 5% of each 5% already accrued, adding up to an additional 12% of the principal owed as interest. Instead, bond issuers can offer a ""coupon bond"". A coupon bond has a coupon rate, which is a percentage of the face value of the bond that is paid periodically (often annually, sometimes semi-annually or even quarterly). A coupon rate helps a company in two ways. First, the calculation is very straightforward; if you need a million dollars and are willing to pay 5% over 10 years, then that's exactly how you issue the bonds; $1million worth with a 5% coupon rate and a maturity date 10 years out. A $100 5% coupon bond with a 10-year maturity, if sold at face value, would cost only $150 over its lifetime, making the total cost of capital only 50% of the principal instead of 62%. Now, that sounds like a bad deal; if the company's paying less, then you're getting less, right? Well yes, but you also get money sooner. Remember the fundamental principle here; money now is worth more than money later, because of what you can do with money between now and later. You do realize a lower overall yield from this investment, but you get returns from it quickly which you can turn around and reinvest to make more money. As such, you're usually willing to tolerate a lower rate of return, because of the faster turnaround and thus the higher present value. The ""Income Yield %"" from your table is also referred to as the ""Flat Yield"". It is a very crude measure, a simple function of the coupon rate, the current quote price and the face value (R/P * V). For the first bond in your list, the flat yield is (.04/114.63 * 100) = 3.4895%. This is a very simple measure that is roughly analogous to what you would expect to make on the bond if you held it for one year, collected the coupon payment, and then sold the bond for the same price; you'd earn one coupon payment at the end of that year and then recoup the principal. The actual present value calculation for a period of 1 year is PV = FV/(1+r), which rearranges to r = FV/PV - 1; plug in the values (present value 114.63, future value 118.63) and you get exactly the same result. This is crude and inaccurate because in one year, the bond will be a year closer to maturity and will return one less coupon payment; therefore at the same rate of return the present value of the remaining payout of the bond will only be $110.99 (which makes a lot of sense if you think about it; the bond will only pay out $112 if you bought it a year from now, so why would you pay $114 for it?). Another measure, not seen in the list, is the ""simple APY"". Quite simply, it is the yield that will be realized from all cash flows from the bond (all coupon payments plus the face value of the bond), as if all those cash flows happened at maturity. This is calculated using the future value formula: FV = PV (1+r/n)nt, where FV is the future value (the sum of the face value and all coupon payments to be made before maturity), PV is present value (the current purchase price), r is the annual rate (which we're solving for), n is the number of times interest accrues and/or is paid (for an annual coupon that's 1), and t is the number of years to maturity. For the first bond in the list, the simple APY is 0.2974%. This is the effective compound interest rate you would realize if you bought the bond and then took all the returns and stuffed them in a mattress until maturity. Since nobody does this with investment returns, it's not very useful, but it can be used to compare the yield on a zero-coupon bond to the yield on a coupon bond if you treated both the same way, or to compare a coupon bond to a CD or other compound-interest-bearing account that you planned to buy into and not touch for its lifetime. The Yield to Maturity, which IS seen, is the true yield percentage of the bond in time-valued terms, assuming you buy the bond now, hold it to maturity and all coupon payments are made on time and reinvested at a similar yield. This calculation is based on the simple APY, but takes into account the fact that most of the coupon payments will be made prior to maturity; the present value of these will be higher because they happen sooner. The YTM is calculated by summing the present values of all payments based on when they'll occur; so, you'll get one $4 payment a year from now, then another $4 in two years, then $4 in 3 years, and $104 at maturity. The present value of each of those payments is calculated by flipping around the future value formula: PV = FV/(1+r)t. The present value of the entire bond (its current price) is the sum of the present value of each payment: 114.63 = 4/(1+r) + 4/(1+r)2 + 4/(1+r)3 + 104/(1+r)4. You now have to solve for r, which is difficult to isolate; the easiest way to find the rate with a computer is to ""goal seek"" (intelligently guess and check).  Based on the formula above, I calculated a YTM of .314% for the first bond if you bought on Sept 7, 2012 (and thus missed the upcoming coupon payment). Buying today, you'd also be entitled to about 5 weeks' worth of the coupon payment that is due on Sept 07 2012, which is close enough to the present day that the discounted value is a rounding error, putting the YTM of the bond right at .40%. This is the rate of return you'll get off of your investment if you are able to take all the returns from it, when you receive them, and reinvest them at a similar rate (similar to having a savings account at that rate, or being able to buy fractional shares of a mutual fund giving you that rate)."

negative: I think Wikipedia offers a very good explanation: A dividend reinvestment program or dividend reinvestment plan (DRIP) is an equity investment option offered directly from the underlying company. The investor does not receive quarterly dividends directly as cash; instead, the investor's dividends are directly reinvested in the underlying equity. The investor must still pay tax annually on his or her dividend income, whether it is received or reinvested. This allows the investment return from dividends to be immediately invested for the purpose of price appreciation and compounding, without incurring brokerage fees or waiting to accumulate enough cash for a full share of stock. So essentially, a dividend reinvestment plan is offered by companies directly, allowing investors to bypass brokerages, and immediately re-invests dividends rather than paying them out in cash. Investopedia also gives a straighforward definition: A plan offered by a corporation that allows investors to reinvest their cash dividends by purchasing additional shares or fractional shares on the dividend payment date.  A DRIP is an excellent way to increase the value of your investment. Most DRIPs allow you to buy shares commission free and at a significant discount to the current share price. Most DRIPS don't allow reinvestments much lower than $10.  I had a hard time finding a comprehensive listing of companies that offered DRPs (or DRIPs), but MyDollarPlan.com offers these suggestions:  Finding a Dividend Reinvestment Plan: Computershare offers one-stop shopping for hundreds of dividend reinvestment plans. They offer a searchable list that can be filtered to easily find a dividend reinvestment plan that fits your needs. You can also use OneShare. Probably the best way to find out if a company offers a dividend reinvestment plan is to visit the company website. Most companies have an Investor Relations area that will highlight the various options available to shareowners. For example: Coca-Cola, Disney, and Wal-Mart. Hope this helps! @YMCbuzz

negative: I have had pension programs with two companies.  The first told you what your benefit would be if you retired at age X with Y years of service. Each year of service got you a percentage of your final years salary. There was a different formula for early retirement, and there was an offset for social security. They were responsible for putting enough money away each year to meet their obligations. Just before I left they did add a new feature. You could get the funds in the account in a lump sum when you left. If you left early you got the money in the account. If you left at retirement age you got the money that was needed to produce the benefit you were promised. Which was based on current interest rates. The second company had a plan where they published the funding formula. You knew with every quarterly statement how much was in your account, and what interest it had earned, and what benefit they estimated you would receive if you stayed until retirement age. This fund felt almost like a defined contribution, because the formula was published. If most people took the lump sum that was the only part that mattered. Both pension plans had a different set of formulas based on marriage status and survivor rules. The interest rates are important because they are used to determine how much money is needed to produce the promised monthly benefit. They are also used to determine how much they need to allocate each year to cover their obligations.  If you can't make the math work you need to keep contacting HR. You need to understand how much should be flowing into the account each month.

negative: You run the regression R_{i,t} = a + bR_{m,t} + e_t, then a + e_t is the variation that isn't shared with the market's variation.

negative: "In general, scholarship income that you receive that is not used for tuition or books must be included in your gross income and reported as such on your tax return.  Scholarship income you receive that is used for those kinds of expenses may be excludable from your gross income.  See this IRS information and this related question. I believe that as represented on the 1098-T, this generally means that if Box 5 (Scholarships and Grants) is greater than Box 1 or 2 (only one of which will be used on your 1098-T), you received taxable scholarship income.  If Box 5 is less than or equal to Box 1/2, you did not receive taxable scholarship income.  This TaxSlayer page draws the same conclusion. However, you should realize that the 1098-T is not what makes you have to pay or not pay taxes.  You incur the taxes by receiving scholarship money, and you may reduce your tax liability by paying tuition.  The 1098-T is simply a record of payments that have already been made. For instance, if you received $10,000 in scholarship money --- that is, actually received checks for that amount or had that amount deposited into your bank account --- then your income went up by $10,000.  If you yourself paid tuition, it is likely that you can exclude the amount of the tuition from your taxable income, reducing the tax you owe (see the IRS page linked above).  However, if you received $10,000 in actual money and in addition your tuition was paid by the scholarship (with money you never actually had in your own bank account), then the entire $10,000 would be taxable.  You do not give enough information in your question to be sure which of these situations is closer to your own.  However, you should be able to decide by looking at your bank account: look at how much money you received and how much you spent on tuition.  If you received more scholarship money than the tuition you paid out of pocket, you owe taxes on the remainder.  (I emphasize that this is just a general rule of thumb and should not be taken as tax advice; you should review the IRS information and/or consult a tax professional to determine what part of your scholarship income is taxable.) In addition, as this (now rather old) article from the New York Society of CPAs notes, ""many colleges and universities prepare 1098-Ts incorrectly and report tuition and related expenses inconsistently"".  This means you should be careful to reconcile the 1098-T with your own financial records of what money you actually received and paid.  When I was in grad school there was a good deal of hand-wringing and hair-pulling each year among the students as we tried to determine what relationship (if any) the 1098-T bore to the financial facts."

negative: I know of no generic formula for determining if an investment property is a good investment, besides the trivial formula. Make sure your income is greater than your expenses, and hope the value of the property doesn't drop. Some people will tell you to expect the monthly rent to be a fixed percentage of the purchase price, but that is a goal not a certainty. It is also impossible to estimate the difficulty renting the property, or how long the roof will last. Taxes can't be predicted, as the value of the house increase, so do the property taxes, but you might not be able to increase the rent.  You can't even predict the quality of the tenant. Will they damage the property? Or skip out early? You will need somebody who knows the local market to estimate the local conditions, and help you determine the estimated costs and income based on the actual property involved.

negative: "My gym has a habit of randomly increasing our monthly payment with a $20 ""Special Fee"" a couple times a year.   This charge was not initiated until after I signed up, and signed authorization for a set monthly fee. The agreement I signed included no wording of this fee, so I have not given them permission to charge me this fee. I also have received no type of notification of this fee prior to it being charged to my credit card on file.   This seems very illegal to me. Am I right? What course of action might I have to get this stopped?"

negative: The key to understanding a mortgage is to look at an amortization schedule.  Put in 100k, 4.5% interest, 30 years, 360 monthly payments and look at the results.  You should get roughly 507 monthly P&I payment.  Amortization is only the loan portion, escrow for taxes and insurance and additional payments for PMI are extra. You'll get a list of all the payments to match the numbers you enter.  These won't exactly match what you really get in a mortgage, but they're close enough to demonstrate the way amortization works, and to plan a budget.  For those terms, with equal monthly payments, you'll start paying 74% interest from the first payment.  Each payment thereafter, that percentage drops. The way this is all calculated is through the time value of money equations.  https://en.wikipedia.org/wiki/Time_value_of_money.  Read slowly, understand how the equations work, then look at the formula for Repeating Payment and Present Value.  That is used to find the monthly payment.   You can validate that the formula works by using their answer and making a spreadsheet that has these columns:  Previous balance, payment, interest, new balance.  Each line represents a month.  Calculate interest as previous balance * APR/12.  Calculate new balance as previous balance minus payment plus interest. Work through all this for a 1 year loan and you will understand a lot better.

negative: "In financial theory, there is no reason for a difference in investor return to exist between dividend paying and non-dividend paying stocks, except for tax consequences.  This is because in theory, a company can either pay dividends to investors [who can reinvest the funds themselves], or reinvest its capital and earn the same return on that reinvestment [and the shareholder still has the choice to sell a fraction of their holdings, if they prefer to have cash]. That theory may not match reality, because often companies pay or don't pay dividends based on their stage of life.  For example, early-stage mining companies often have no free cashflow to pay dividends [they are capital intensive until the mines are operational]. On the other side, longstanding companies may have no projects left that would be a  good fit for further investment, and so they pay out dividends instead, effectively allowing the shareholder to decide where to reinvest the money. Therefore, saying ""dividend paying""/""growth stock"" can be a proxy for talking about the stage of life + risk and return of a company. Saying dividend paying implies ""long-standing blue chip company with relatively low capital requirements and a stable business"". Likewise ""growth stocks"" [/ non-dividend paying] implies ""new startup company that still needs capital and thus is somewhat unproven, with a chance for good return to match the higher risk"". So in theory, dividend payment policy makes no difference. In practice, it makes a difference for two reasons: (1) You will most likely be taxed differently on selling stock vs receiving dividends [Which one is better for you is a specific question relying on your jurisdiction, your current income, and things like what type of stock / how long you hold it]. For example in Canada, if you earn ~ < $40k, your dividends are very likely to have a preferential tax treatment to selling shares for capital gains [but your province and specific other numbers would influence this]. In the United States, I believe capital gains are usually preferential as long as you hold the shares for a long time [but I am not 100% on this without looking it up]. (2) Dividend policy implies differences in the stage of life / risk level of a stock. This implication is not guaranteed, so be sure you are using other considerations to determine whether this is the case.  Therefore which dividend policy suits you better depends on your tax position and your risk tolerance."

negative: "The fundamental concept of the time value of money is that money now is worth more than the same amount of money later, because of what you can do with money between now and later. If I gave you a choice between $1000 right now and $1000 in six months, if you had any sense whatsoever you would ask for the money now. That's because, in the six months, you could use the thousand dollars in ways that would improve your net worth between now and six months from now; paying down debt, making investments in your home or business, saving for retirement by investing in interest-bearing instruments like stocks, bonds, mutual funds, etc. There's absolutely no advantage and every disadvantage to waiting 6 months to receive the same amount of money that you could get now. However, if I gave you a choice between $1000 now and $1100 in six months, that might be a harder question; you will get more money later, so the question becomes, how much can you improve your net worth in six months given $1000 now? If it's more than $100, you still want the money now, but if nothing you can do will make more than $100, or if there is a high element of risk to what you can do that will make $100 that might in fact cause you to lose money, then you might take the increased, guaranteed money later. There are two fundamental formulas used to calculate the time value of money; the ""future value"" and the ""present value"" formulas. They're basically the same formula, rearranged to solve for different values. The future value formula answers the question, ""how much money will I have if I invest a certain amount now, at a given rate of return, for a specified time""?. The formula is FV = PV * (1+R)N, where FV is the future value (how much you'll have later), PV is the present value (how much you'll have now), R is the periodic rate of return (the percentage that your money will grow in each unit period of time, say a month or a year), and N is the number of unit periods of time in the overall time span. Now, you asked what ""compounding"" is. The theory is very simple; if you put an amount of money (the ""principal"") into an investment that pays you a rate of return (interest), and don't touch the account (in effect reinvesting the interest you earn in the account back into the same account), then after the first period during which interest is calculated and paid, you'll earn interest on not just the original principal, but the amount of interest already earned. This allows your future value to grow faster than if you were paid ""simple interest"", where interest is only ever paid on the principal (for instance, if you withdrew the amount of interest you earned each time it was paid). That's accounted for in the future value formula using the exponent term; if you're earning 8% a year on your investment, then after 1 year you'll have 108% of your original investment, then after two years you'll have 1.082 = 116.64% (instead of just 116% which you'd get with simple interest). That .64% advantage to compounding doesn't sound like much of an advantage, but stay tuned; after ten years you'll have 215.89% (instead of 180%) of your original investment, after 20 you'll have 466.10% (instead of 260%) and after 30 your money will have grown by over 1000% as opposed to a measly 340% you'd get with simple interest. The present value formula is based on the same fundamental formula, but it's ""solved"" for the PV term and assumes you'll know the FV amount. The present value formula answers questions like ""how much money would I have to invest now in order to have X dollars at a specific future time?"". That formula is PV = FV / (1+R)N where all the terms mean the same thing, except that R in this form is typically called the ""discount rate"", because its purpose here is to lower (discount) a future amount of money to show what it's worth to you now. Now, the discount rate (or yield rate) used in these calculations isn't always the actual yield rate that the investment promises or has been shown to have over time. Investors will calculate the discount rate for a stock or other investment based on the risks they see in the company's financial numbers or in the market as a whole. The models used by professional investors to quantify risk are rather complex (the people who come up with them for the big investment banks are called ""quants"", and the typical quant graduates with an advanced math degree and is hired out of college with a six-figure salary), but it's typically enough for the average investor to understand that there is an inherent risk in any investment, and the longer the time period, the higher the chance that something bad will happen that reduces the return on your investment. This is why the 30-year Treasury note carries a higher interest rate than the 10-year T-note, which carries higher interest than the 6-month, 1-year and 5-year T-bills. In most cases, you as an individual investor (or even an institutional investor like a hedge fund manager for an investment bank) cannot control the rate of return on an investment. The actual yield is determined by the market as a whole, in the form of people buying and selling the investments at a price that, coupled with the investment's payouts, determines the yield. The risk/return numbers are instead used to make a ""buy/don't buy"" decision on a particular investment. If the amount of risk you foresee in an investment would require you to be earning 10% to justify it, but in fact the investment only pays 6%, then don't buy it. If however, you'd be willing to accept 4% on the same investment given your perceived level of risk, then you should buy."

negative: The question states :- Our insurance company is offering a 30% discount on an $8200/year   commercial policy, if we install sprinklers. The insurance is paid in   two installments. ... This appears to mean six-monthly payments, so I'll make some comparison calculations using six-monthly loan repayments to keep things simple. Without the loan or sprinklers the insurance costs $4100 every six months. Using this loan payment formula, the calculation below shows, with the 30% discounted insurance, sprinkler maintenance and loan repayment, you would be paying $4655.28 every six months.  The discount required to break even is 43.5%.  I.e. rearranging the equation :-  Alternatively, with the discount of 30% you would break even if the six-monthly repayment amount was $1030.  Solving the payment equation for s gives an equation for the loan :-  So with the 30% discount you would break even if the loan required was $25989. Checking by back-calculating the periodic payment amount, a :-  Likewise we can keep the loan at $40000 and solve for t to find the break-even loan term :-  (Note, in this formula Log denotes the natural logarithm.)  Now we can set some values :-  So with break-even payments the $40000 loan is paid off in just under 65.5 years.  I.e. checking :-  This just beats the $4100 cost of proceeding without the sprinklers. Notes If your loan repayment was monthly it would reduce the cost of the loan slightly.  The periodic interest rate is calculated from the APR according to the method used in the EU and in some cases in US.  The calculations above were run using Mathematica.

negative: There are a few ways to look at this question. Assumptions. Per the original post's assumptions, this answer: In other words, if the owner paid the mortgage on its original schedule, the deal could boil down to a $ 40,000 up-front payment, in exchange for $ 200,000 of equity after 30 years.  Or the deal could boil down to a $ 40,000 up-front payment, in exchange for a $ 810.70 monthly payment starting in 30 years. While the owner is paying down the mortgage, the return on equity is the principal payment divided by the equity.  The principal payment is the net rent minus non-financing costs and interest, so it is actually a profit. The initial return on equity is 6.321 % APR, or 6.507 % APY.  This is calculated by dividing the $ 210.70 monthly principal payment by the initial $ 40,000 equity, and converting from monthly return to annual return. After 30 years, the return on equity is 4.864 % APR, or 4.974 % APY.  This is calculated by dividing the $ 810.70 monthly cash flow (which is no longer reduced by mortgage payments) by the $ 200,000 equity after 30 years, and converting from monthly return to annual return. The cap rate is the same as the return on equity in the absence of debt.  In this example, 4.864 % APR, or 4.974 % APY. The return on equity declines from 6.507 % APY initially to 4.974 % APY after 30 years. This is because the cap rate exceeds the note rate (4.974 % APY vs. 4.594 % APY), and the leverage decreases from 5x to 1x. The weighted average compound annual growth rate of the equity during the 30 years is 5.511 % APY.  Per the original poster's answer, this is computed by taking the 30th root of the 5-fold increase in equity.  Because the owner made no extra principal payments (besides those already discussed), the relevant amounts are the initial $ 40,000 owner payment and the final $ 200,000 owner equity.  5.511 % APY corresponds to a 5.377 % APR. The internal rate of return if the owner never sells can be computed by treating the deal as a $ 40,000 up-front payment, in exchange for an $ 810.70 monthly payment starting in 30 years.  The internal rate of return (IRR) is not a very useful number, because it assumes that you can somehow reinvest the eventual dividends at the same rate.  In this example, the IRR is 5.172 % APR, or 5.296  % APY.  In this example, the IRR is calculated by (iteratively) finding an interest rate for which (initial investment) * (1 + IRR) ^ (number periods before dividends start) = (periodic dividend) / (IRR - growth rate of dividend).  For example: $ 40,000 * (1.004309687)^360 = $ 810.70 / (0.004309687 - 0) = $ 188,111 I then converted the 0.431 % monthly IRR to an annual IRR. The deal can be thought of as a return on equity, plus a return on paying down the mortgage. When computing the return from paying down the mortgage, the initial equity is irrelevant.  It does not matter whether you start with a $ 160,000 mortgage on a $ 160,000 property, a $ 160,000 mortgage on a $ 200,000 property, or a $ 160,000 mortgage on a $ 1,000,000 property.  All that matters is the note rate on the mortgage, which is the applicable compound interest rate. The return on paying down the mortgage equals the note rate of the mortgage.  For a 4.5% note rate, this works out to a 4.594% annual percentage yield (APY). You can confirm this by looking at your amortization schedule.  Suppose you have a $ 160,000 mortgage with a fixed 4.5% APR note rate for 360 months.  Your monthly payment is $ 810.70.  In the first month, $ 600 goes toward interest, and $ 210.70 reduces the principal.  In other words, the $ 210.70 principal payment eliminated the need for a $ 810.70 payment 30 years later.  Notice that: . $ 210.70 * (1 + 0.045 / 12)^360 = $ 210.70 * (1.00375)^360 = $ 210.70 * 3.8477 = $ 810.71 which is within rounding error of $ 810.70. The interest rate is 3/8 % per month, which is an APR of 4.5%, and an APY of 4.594 %.

negative: Many folks use bonds to diversify their portfolio since bonds rise and fall in value at different times and for different reasons than stocks. Bonds pay interest on a regular basis (usually monthly or quarterly) and so some people invest in bonds in order to match the interest payments to some regular expense they might have. The interest payment does not change (fixed income).  For individual bonds, there is a maturity date at which you can expect to receive the face value of the bond (the issuer's creditworthiness is important here). You can make a little money on a bond by buying it when its value is lower than its face value and either selling later for a higher value, or waiting for it to mature.  Often the minimum investment for a single bond is high, so if you don't have a large enough amount, you can still get the performance of bonds through a bond fund. These do not mature, so you don't have a guarantee of a return of your investment. However, they have access to more bonds than retail investors, so the funds can keep your money more fully invested. If you don't need the income, you can reinvest the dividends and have a little extra capital growth this way.

negative: The general concept is that your money will grow at an accelerating rate because you start getting interest paid on your returns in addition to the original investment.  As a simple example, assume you invest $100 and get 10% interest per year paid annually.   -At the end of the first year you have your $100 + $10 interest for a total of $110. -So you start the second year with $110 and so 10% would be $11 for a total of $121. -The third year you start with $121 so 10% would be $12.10 for a total of $133.10 See how the amount it goes up each year increases? If we were talking a higher initial amount or a larger number of years that can really add up. That is essence is compound interest. Most of the complicated looking formulas you see out there for compound interest are just shortcuts so you don't have to iteratively go through the above exercise a bunch of times to find out how much you would have after some number of years. This formula tells you how much you would have(A) after a certain number of years(t)  at a given interest rate(r) assuming they pay interest n times per year, for example you would use 12 for n if it paid interest monthly instead of yearly. P represents the  amount you started out with.   If you keep investing monthly (as shown in your example) instead of just depositing it and letting it sit, you have to use a more complicated formula. Finance people refer to this as calculating the future value of an annuity.  That formula looks like this: A = PMT [((1 + r)N - 1) / r] x (1+r)  A : Is the amount you would have at the end of the time period.   N : The number of compounding periods (months if you get interest calculated monthly)   PMT : The total amount you are putting in each period (N)    r: Just like before, the interest rate you are getting paid. Be sure to adjust this to a monthly number if N represents months (divide APR by 12)* *Most interest rates are quoted as APR, which is the annualized interest rate not counting compounding. Don't confuse this with APY, which has compounding built into it and is not appropriate for use in this formula. Inserting your example: r (monthly interest rate) = 15% APR / 12 = .0125 n = 30 years * 12 months/year = 360 months   A = $150 x [((1 + .0125)360 - 1) / .0125] x (1+.0125) A = $1,051,473.09 (rounded)

negative: The reason it's broken out is very specific: this is showing you how much interest accrued during the month.  It is the only place that's shown, typically. Each month's (minimum) payment is the sum of [the interest accrued during that month] and [some principal], say M=I+P, and B is your total loan balance.  That I is fixed at the amount of interest that accrued that month - you always must pay off the accrued interest.  It changes each month as some of the principal is reduced; if you have a 3% daily interest rate, you owe (0.03*B*31) approximately (plus a bit as the interest on the interest accrues) each month (or *30 or *28).  Since B is going down constantly as principal is paid off, I is also going down. The P is most commonly calculated based on an amortization table, such that you have a fixed payment amount each month and pay the loan off after a certain period of time.  That's why P changes each month - because it's easier for people to have a constant monthly payment M, than to have a fixed P and variable I for a variable M. As such, it's important to show you the I amount, both so you can verify that the loan is being correctly charged/paid, and for your tax purposes.

negative: Depending on who you have the loan through and how they figure the interest charges (whether daily, monthly, bi-monthly, etc. normally monthly I would assume), your interest is probably figured either daily or once a month.   Let's assume that it is figured daily, otherwise it wouldn't make sense to make bi-weekly payments.   At 4% Annual Interest on a $150,000 home loan the interested added each day is about $16.44, but it doesn't stop there because it is compounding interest daily so the next day it becomes 4% of 150,0016.44 (which is negligibly larger amount) and they will tack on another $16.44. So what will happen is that the amount of interest you owe grows rather quickly, especially if you miss a monthly payment.  Everyone knows that the faster you pay something off the less interest you pay, but not everyone knows the formula for compounding interest.  a quick Google search rendered this site with a simple explanation Compound Interest Formula  unfortunately this formula doesn't take into account the payments being made. The big thing with making your payments bi-weekly rather than a bigger payment once a month is that you pay off some of that principle right away and it won't collect interest for 14 more days. if the interest is only calculated once a month, make your full payment before the interest is calculated, the same goes for your credit cards.

negative: "@fredsbend, Hope this helps!  ""I understand that a reverse mortgage can be paid out in two ways: A lump sum and monthly payments. I figure that if you take the lump sum, eventually, the bank wants you to start paying it back."" Answer:   Actually, there are 3 payout options, or 4 if you consider a combination payout as another one. There's a lump sum, a line of credit, or the monthly payout, or a combination.  ""I figure that if you take the monthly payments, eventually, the bank stops paying out and wants you to pay it back. In both situations, interest accrues and this is how the bank makes money off of the deal"".  Answer: The only time the monthly payments would stop would be if the borrower defaults on the lenders' terms or they no longer live at home. You are right though, and interest does accrue on whichever payment is decided on. I'm not sure how the lender makes money, probably by the interest, but I know borrowers are protected against high rates and owing more than your house. Here's an article I found that goes over the protections more in detail: https://www.americanadvisorsgroup.com/news/6-consumer-protections-reverse-mortgage-loan-borrowers.  ""But what determines when you have to begin paying back the reverse mortgage? Some sources online seem to say that it's based only on if you die or would like to sell/move. That can't be right in all situations, because you could end up with a massive debt on a property more than its value.""  Answer: There are a lot of protections or regulations in place to protect anyone who takes out a reverse mortgage. One being, you can't owe MORE than your house is valued at during the time of repayment, a reverse mortgage is a non-recourse loan. In the instance that your house is less than you owe, you either sell the home and the proceeds are used to pay the loan and you keep the rest OR if you owe more than the house proceeds of the home go to the lender. Either way, you're not left paying for a ""mortgage"" without the house. In the case the parent, grandparent passes, then the heirs would have a choice of either paying back the reverse mortgage in payments, OR they can sell the house, heirs are protected during this as well to make sure they're not left with major debt in case of anything.  Is there a formula to figure out when the bank stops the monthly payments and then wants it back?  **Answer:**The amount becomes due if loan terms are not met, but the lender will discuss the options if it comes to that.  Is there a different formula for when the lump sum would have to be paid back?""  Answer: Each payout option has the same terms and the same pay back terms. As long as terms are met, the lender can't ask for early repayment."

negative: "As JoeTaxpayer says, there's a lot you can do with just the stock price. Exploring that a bit: Stock prices are a combination of market sentiment and company fundamentals. Options are just a layer on top of that. As such, options are mostly formulaic, which is why you have a hard time finding historical option data -- it's just not that ""interesting"", technically. ""Mostly"" because there are known issues with the assumptions the Black-Scholes formula makes. It's pretty good, and importantly, the market relies on it to determine fair option pricing. Option prices are determined by: Relationship of stock price to strike. Both distance and ""moneyness"". Time to expiration. Dividends. Since dividend payments reduce the intrinsic value of a company, the prospect of dividend payments during the life of a call option depresses the price of the option, as all else equal, without the payments, the stock would be more likely to end up in the money. Reverse the logic for puts. Volatility. Interest rates. But this effect is so tiny, it's safe to ignore. #4, Volatility, is the biggie. Everything else is known. That's why option trading is often considered ""volatility trading"". There are many ways to skin this cat, but the result is that by using quoted historical values for the stock price, and the dividend payments, and if you like, interest rates, you can very closely determine what the price of the option would have been. ""Very closely"" depending on your volatility assumption. You could calculate then-historical volatility for each time period, by figuring the average price swing (in either direction) for say the past year (year before the date in question, so you'd do this each day, walking forward). Read up on it, and try various volatility approaches, and see if your results are within a reasonable range. Re the Black-Scholes formula,  There's a free spreadsheet downloadable from http://optiontradingtips.com. You might find it useful to grab the concept for coding it up yourself. It's VBA, but you can certainly use that info to translate in your language of choice. Or, if you prefer to read Perl, CPAN has a good module, with full source, of course. I find this approach easier than reading a calculus formula, but I'm a better developer than math-geek :)"

negative: You must not be from around these parts.  AT&T & Verizon have really done an excellent job at nothing.  I mange 25 lines for the company I work at.  having that many lines, I see some fun things.  We have at times been with both AT&T, Verizon, and T-Mobile.  Of the 3 only T-Mobile has the honor of more than 3 consecutive months without a billing error.  Infact our 2 years with T-Mobile, there was only 3 billing errors.  AT&T had errors monthly, Verizon was as bad.  Signal, of course varies from one local to another, but here all 3 suck the hind tit.  I have nothing from my experience with AT&T and Verizon that I could say positively about the quality of the service.

negative: An amortization schedule is often used to produce identical payments for the term (repayment period) of a loan, resulting in the principal being paid off and the debt retired at the end of the loan. This is in contrast to an interest only, or balloon loan. These loans require little or no payment against the balance of the loan, requiring the loan to be paid indefinitely if there is no term, or requiring the loan to be entirely paid off from cash or a new loan at the end of the term. A basic amortization formula can be derived from the compound interest formula:   This formula comes from the Wikipedia article on amortization. The basics of the formula are the periodic payment amount, A (your monthly payment), can be determined by the principal loan, P, the rate, r, and the number of payments, n.  Lenders lend money to make a profit on the interest. They'd like to get back all the money they lent out. Amortization schedules are popular because the fixed low payments make it easier for borrowers to pay the loan off eventually. They also tend to be very profitable for lenders, especially at the start of the term, because they make a lot of profit on interest, just like the start of your mortgage. The principal of a mortgage has more meaning than the principal of a revolving debt credit card. The mortgage principal is fixed at the start, and represents the value of the collateral property that is your home. You could consider the amount of principal paid to be the percentage of your home that you actually own (as part of your net worth calculation).  A credit card has a new balance each month depending on how much you charge and how much you pay off. Principal has less meaning in this case, because there is no collateral to compare against, and the balance will change monthly. In this case, the meaning of the amortization schedule on your credit card is how long it will take you to pay off the balance if you stop charging and pay at the proscribed payment level over the term described. Given the high interest rate on credit cards, you may end up paying twice as much for goods in the long run if you follow your lenders schedule. Amortizing loans are common for consumer loans, unless a borrower is seeking out the lowest possible monthly payment. Lenders recognize that people will eventually die, and want to be paid off before that happens. Balloon and interest only bonds and loans are more commonly issued by businesses and governments who are (hopefully) investing in capital improvements that will pay off in the long run. Thousands of people and businesses have gone bankrupt in this financial crisis because their interest only loans reached term, and no one was willing to lend them money anymore to replace their existing loan.

negative: If you are putting down less than 20% expect to need to pay PMI.  When you first applied they should have described you a group of options ranging from minimal to 20% down. The monthly amounts would have varied based on PMI, down payment, and interest rate. The maximum monthly payment for principal, interest, taxes, and insurance will determine the maximum loan you can get. The down payment determines the price of the house above the mortgage amount.  During the most recent real estate bubble, lenders created exotic mortgage options to cover buyers who didn't have cash for a down-payment; or not enough income for the principal and interest, or ways to sidestep PMI. Many of these options have disappeared or are harder to get. You need to go back to the bank and get more information on your different options, or find a lender broker who will help you.

negative: "In almost all cases, gifts from employers are considered taxable compensation, based on the employer-employee nature of the relationship. Furthermore, cash gifts are always considered to be intended as wages, regardless of how you receive the money. Furthermore, regardless of whether you expect to receive anything in return (such as contractual consideration) or whether the amounts are large enough to be declared as taxable personal gifts, it is likely that the IRS would consider these payments to be ""disguised wages"", as these payments would fail several tests that the IRS uses to determine whether benefits provided by the employer are non-taxable, including: I'd recommend reviewing IRS publication 535 here, as well as publication 15-B here for more on what constitutes taxable wages & benefits. It seems very unlikely to me that you could make a persuasive legal defense in which you claimed to be working full-time for $60.00 per year and just happened to be receiving large personal gifts of $130,000.00. In my opinion it seems much more likely that these payments would be found to be taxable wages for services rendered."

negative: Slide 1 Blogspot: NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud - FC2 Knowhow deanciana Slide 2 NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton saeo.net — Current Class Dates (subject to change): Scheduled as Needed based on Student Demand. Email us atonlinetrain@nortonaudits.com if you are interested in this course. Description - This is an advanced-level class that takes an in-depth examination of severe noncompliance, clinical data fabrication and falsification, scientific misconduct and fraud cases. The course focus is on developing skills for preventing fraud and misconduct and preparing clinical research professionals to better handle severe noncompliance. Slide 3 Source: saeo.net #NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton #norton scientific reblog  clintonmccage: NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton Current Class Dates (subject to change):  Scheduled as Needed based on Student Demand. Email us atonlinetrain@nortonaudits.com if you are interested in this course.  Slide 4 Description - This is an advanced-level class that takes an in-depth examination of severe noncompliance,clinical data fabrication and falsification, scientific misconduct and fraud cases. The course focus is on developing skills for preventing fraud and misconduct and preparing clinical research professionals to better handle severe noncompliance. Source: saeo.net #NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton #norton scientific reblog  eddiemccrane: Slide 5 NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton Current Class Dates (subject to change):  Scheduled as Needed based on Student Demand. Email us atonlinetrain@nortonaudits.com if you are interested in this course.  Description - This is an advanced-level class that takes an in-depth examination of severe noncompliance, clinical data fabrication and falsification, scientific misconduct and fraud cases. The course focus is on developing skills for preventing fraud and misconduct and preparing clinical research professionals to better handle severe noncompliance. Slide 6 Source: saeo.net #NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton #norton scientific 1 note reblog  pittturvey: Norton Scientific : Blogspot | Facebook Fraud Prevention | NORTON SCIENTIFIC SCAM-Detection and Prevention of Clinical Research Fraud and Misconduct A Norton : Social-bookmarking.net Current Class Dates (subject to change): Scheduled as Needed based on Student Demand. Email us atonlinetrain@nortonaudits.com if you are interested in this course. Slide 7 Description - This is an advanced-level class that takes an in-depth examination of severe noncompliance,clinical data fabrication and falsification, scientific misconduct and fraud cases. The course focus is on developing skills for preventing fraud and misconduct and preparing clinical research professionals to better handle severe noncompliance. Slide 8 Class Agenda/Modules - Instructors Make a Difference Defining Clinical Research Fraud and Misconduct Evaluation of Case History R.E.S.E.A.R.C.H. TM Skills Program Advanced Auditing and Monitoring Skills for Prevention Case Development

negative: There is no interest outstanding, per se.  There is only principal outstanding.  Initially, principal outstanding is simply your initial loan amount. The first two sections discuss the math needed - just some arithmetic. The interest that you owe is typically calculated on a monthly basis.  The interested owed formula is simply (p*I)/12, where p is the principal outstanding, I is your annual interest, and you're dividing by 12 to turn annual to monthly. With a monthly payment, take out interest owed.  What you have left gets applied into lowering your principal outstanding.  If your actual monthly payment is less than the interest owed, then you have negative amortization where your principal outstanding goes up instead of down. Regardless of how the monthly payment comes about (eg prepay, underpay, no payment), you just apply these two calculations above and you're set.  The sections below will discuss these cases in differing payments in detail. For a standard 30 year fixed rate loan, the monthly payment is calculated to pay-off the entire loan in 30 years.  If you pay exactly this amount every month, your loan will be paid off, including the principal, in 30 years.  The breakdown of the initial payment will be almost all interest, as you have noticed.  Of course, there is a little bit of principal in that payment or your principal outstanding would not decrease and you would never pay off the loan. If you pay any amount less than the monthly payment, you extend the duration of your loan to longer than 30 years.  How much less than the monthly payment will determine how much longer you extend your loan.  If it's a little less, you may extend your loan to 40 years.  It's possible to extend the loan to any duration you like by paying less.  Mathematically, this makes sense, but legally, the loan department will say you're in breach of your contract. Let's pay a little less and see what happens.  If you pay exactly the interest owed = (p*I)/12, you would have an infinite duration loan where your principal outstanding would always be the same as your initial principal or the initial amount of your loan.   If you pay less than the interest owed, you will actually owe more every month.  In other words, your principal outstanding will increase every month!!!  This is called negative amortization.  Of course, this includes the case where you make zero payment.  You will owe more money every month. Of course, for most loans, you cannot pay less than the required monthly payments.  If you do, you are in default of the loan terms. If you pay more than the required monthly payment, you shorten the duration of your loan.  Your principal outstanding will be less by the amount that you overpaid the required monthly payment by.  For example, if your required monthly payment is $200 and you paid $300, $100 will go into reducing your principal outstanding (in addition to the bit in the $200 used to pay down your principal outstanding).  Of course, if you hit the lottery and overpay by the entire principal outstanding amount, then you will have paid off the entire loan in one shot! When you get to non-standard contracts, a loan can be structured to have any kind of required monthly payments.  They don't have to be fixed.   For example, there are Balloon Loans where you have small monthly payments in the beginning and large monthly payments in the last year.   Is the math any different?  Not really - you still apply the one important formula, interest owed = (p*I)/12, on a monthly basis.  Then you break down the amount you paid for the month into the interest owed you just calculated and principal.  You apply that principal amount to lowering your principal outstanding for the next month. Supposing that what you have posted is accurate, the most likely scenario is that you have a structured 5 year car loan where your monthly payments are smaller than the required fixed monthly payment for a 5 year loan, so even after 2 years, you owe as much or more than you did in the beginning!  That means you have some large balloon payments towards the end of your loan.  All of this is just part of the contract and has nothing to do with your prepay. Maybe I'm incorrect in my thinking, but I have a question about   prepaying a loan. When you take out a mortgage on a home or a car   loan, it is my understanding that for the first years of payment you   are paying mostly interest. Correct. So, let's take a mortgage loan that allows prepayment without penalty.   If I have a 30 year mortgage and I have paid it for 15 years, by the   16th year almost all the interest on the 30 year loan has been paid to   the bank and I'm only paying primarily principle for the remainder of   the loan. Incorrect.  It seems counter-intuitive, but even in year 16, about 53% of your monthly payment still goes to interest!!!  It is hard to see this unless you try to do the calculations yourself in a spreadsheet. If suddenly I come into a large sum of money and decide I want to pay   off the mortgage in the 16th year, but the bank has already received   all the interest computed for 30 years, shouldn't the bank recompute   the interest for 16 years and then recalculate what's actually owed in   effect on a 16 year loan not a 30 year loan? It is my understanding   that the bank doesn't do this. What they do is just tell you the   balance owed under the 30 year agreement and that's your payoff   amount. Your last sentence is correct.  The payoff amount is simply the principal outstanding plus any interest from (p*I)/12 that you owe.  In your example of trying to payoff the rest of your 30 year loan in year 16, you will owe around 68% of your original loan amount. That seems unfair. Shouldn't the loan be recalculated as a 16 year   loan, which it actually has become? In fact, you do have the equivalent of a 15 year loan (30-15=15) at about 68% of your initial loan amount.  If you refinanced, that's exactly what you would see.  In other words, for a 30y loan at 5% for $10,000, you have monthly payments of $53.68, which is exactly the same as a 15y loan at 5% for $6,788.39 (your principal outstanding after 15 years of payments), which would also have monthly payments of $53.68. A few years ago I had a 5 year car   loan. I wanted to prepay it after 2 years and I asked this question to   the lender. I expected a reduction in the interest attached to the car   loan since it didn't go the full 5 years. They basically told me I was   crazy and the balance owed was the full amount of the 5 year car loan.   I didn't prepay it because of this. That is the wrong reason for not prepaying.  I suspect you have misunderstood the terms of the loan - look at the Variable Monthly Payments section above for a discussion.   The best thing to do with all loans is to read the terms carefully and do the calculations yourself in a spreadsheet.  If you are able to get the cashflows spelled out in the contract, then you have understood the loan.

negative: tl;dr: The CNN Money and Yahoo Finance charts are wildly inaccurate. The TD Ameritrade chart appears to be accurate and shows returns with reinvested dividends. Ignoring buggy data, CNN most likely shows reinvested dividends for quoted securities but not for the S&P 500 index. Yahoo most likely shows all returns without reinvested dividends. Thanks to a tip from Grade Eh Bacon, I was able to determine that TD Ameritrade reports returns with reinvested dividends (as it claims to do). Eyeballing the chart, it appears that S&P 500 grew by ~90% over the five year period the chart covers. Meanwhile, according to this S&P 500 return estimator, the five year return of S&P 500, with reinvested dividends, was 97.1% between July 2012 to July 2017 (vs. 78.4% raw returns). I have no idea what numbers CNN Money is working from, because it claims S&P 500 only grew about 35% over the last five years, which is less than half of the raw return. Ditto for Yahoo, which claims 45% growth. Even stranger still, the CNN chart for VFINX (an S&P 500 index fund) clearly shows the correct market growth (without reinvesting dividends from the S&P 500 index), so whatever problem exists is inconsistent:  Yahoo also agrees with itself for VFINX, but comes in a bit low even if your assume no reinvestment of dividends (68% vs. 78% expected); I'm not sure if it's ever right.  By way of comparison, TD's chart for VFINX seems to be consistent with its ABALX chart and with reality:  As a final sanity check, I pulled historical ^GSPC prices from Yahoo Finance. It closed at $1406.58 on 27 Aug 2012 and $2477.55 on 28 Aug 2017, or 76.1% growth overall. That agrees with TD and the return calculator above, and disagrees with CNN Money (on ABALX). Worse, Yahoo's own charts (both ABALX and VFINX) disagree with Yahoo's own historical data.

negative: "Paypal linked with my bank account. 1.Can I use my Saving bank account to receive payments from my clients? Or is it necessary to open a current account? Yes you can get funds into your savings account. However it is advisable to keep a seperate account as it would help with your IT Returns. 2.I will be paying a certain % as commission on every sales to a couple of sales guys (who are not my employees but only working on   commission). Can I show this as an expense in my IT returns? As you are earning as freelancer, you are eligible for certain deductions like Phone calls, Laptop, other hardware, payments to partners. It is important that you maintain a book of records. An accountant for a small fee of Rs 5 K should be able to help you. In the Returns you have to show Net income after all these deductions, there is no place to enter expenses.   3.Since I will be receiving all the payments in Euros so am I falling under a category of ""Exporter of services""? The work you are doing can be Free Lancing.    4.Do I need an Import Export Code (IEC) for smoothly running this small business? You can run this without one as Free lancing. IEC would be when you grow big and are looking for various benefits under tax and pay different taxes and are incorporated as a company."

negative: @JoeTaxpayer's answer outlines how to value it. Some other considerations: As I understand it, some public pensions may be tax-free if you still live in the state that is paying the pension. E.g. when a Massachusetts teacher receives pension, it is exempt from state taxes, but if that person moves to Vermont he will have to pay Vermont income tax on those payments. So if you plan to stay in the state post-retirement, this provides additional value. Pension payments aren't fully guaranteed by the PBGC. And not all pension plans are fully funded. Depending on the political and economic environment when you hit retirement, your retirement plan could suffer. (And if you aren't working, you may not have a union vote any more when the other working members are voting on contract amendments that affect pensions.) I'm not certain of all of the rules, but I hear news reports from time to time that formulas like what you've posted in the original question are changed through negotiation with the union. If you make an employment decision using the formula in year X and then the formula changes in year X+10, your expected pension payment will change.

negative: Edit: I a in the United States, seek advice from someone who is also in Australia.  I am getting about 5.5% per year by investing in a fund (ticker:PGF) that, in turn, buys preferred stock in banks. Preferred stock acts a bit like a bond and a bit like a stock.  The price is very stable. However, a bank account is FDIC insured (in the USA) and an investment is not. I use the Reinvestment program at Scottrade so that the monthly dividends are automatically reinvested with no commission. However I do not know if this is available outside of the United States.  Investing yealds greater returns but exposes you to greater risk. You have to know your risk tolerance.