<prompt> Human: After seeing questions or comments about things related to the question in the title one too many times, I finally wrote up an explanation of how interest and amortization and stuff works on installment loans because I havent run across one and want something I can link to in the future.There is a graphical version of the below at I encourage looking at that instead because its prettier. However, I will attempt to reproduce the content below. How does loan interest workSuppose you take out a loan to pay for college mostly, car, house, etc. Student loans have some unusual aspects like income-driven repayment plans, deferment, and forebearance that wont be covered. Credit cards also do not particularly work as described.Congratulations, you are now the proud owner of a ten year, 10,000 loan at 6 APR!And then the first statement arrives, but it says this: Interest: 50.00 Principal: 61.02 Payment due: 111.02And you think Why is the interest so high? 50 is 45 of my payment! I thought my interest was 6?! Time for some graphs! Except not, because youre not looking at the good version of this. :-What doesnt happen is an even breakdown of principal and interest throughout the life of the loan, unchanging month to month.Instead, the portion of your payment that goes toward interest and principal changes over time.It starts off with a lot going toward interest, but as the loan progresses that amount decreases; at the end of the loan, very little of your payments is going toward interest.So sure, the first statement says Interest: 50.00 Principal: 61.02 Payment due: 111.02but the last one will say Interest: 0.55 Principal: 110.47 Payment due: 111.02Thats much friendlier. So what does actually happen?First, figure out how much interest we need to pay.Multiply the current balance by the interest rate divided by 12 because 12 months. For the example loan: 10,000 balance 6 interest 12 months 50So 50 of our first payment will go toward interest. The remainder goes toward principal: 111.02 - 50 61.02 toward principal for the first month.That principal payment reduces your balance. So for the following month, we compute: 10,000 starting balance - 61.02 payment 612 9,938.98 balance 0.5 49.69 interest owed 111.02 payment - 49.69 61.33 principal paid during second monthNote that there is slightly more going toward principal in the second month than there was in the first. That will reduce the balance more for the third month than the first months payment reduced the balance for the second; that will correspondingly increase the amount of payment going toward principal in the third month by more than the difference between the first and second months.In other words, the payoff accelerates. This is the doing of compound interest! So how do we know the payment?I like to think of the size of the monthly payment being set so that if you repeat that process every month for the desired length of the loan, you will finish with exactly a 0 balance.To figure it out, use an online loan calculator or the PMT function in your favorite spreadsheet. Or: payment principal rm 1 - 1 rm-12y rm APR12 i.e. monthly interest y number of years in loan A word on prepaymentsA prepayment is an extra, principal-only payment you make above the required amount the 111.02.Prepayments reduce your balance for the following month just like the principal portion of your normal payment, and will speed up repayment of the loan and reduce the total amount of interest paid.Note that they will not decrease the monthly payments you make in the future, unless you can recast the loan. Also note that some loan servicers also let you pay aheadthat is just paying early and not a prepayment in the sense I mean here. Thats almost never what you want, so make sure any extra payments youre making are actually being applied in the right place. Ive given you the tools to double check your loan servicers math. :-Suppose we are considering paying 30 extra per month as a prepayment on the example 10K loan.One way to look at this is I am only paying about 25 extra; how much difference could that make? But from another point of view, you are increasing the amount of principal you are paying that month by almost 50.In fact, if you could prepay 60, you would basically be paying for the second months principal now. That would be like cutting the second months payment out of the schedule completely: the loan would end one month early, and, in the long run, you would not pay the interest that would have occurred in the second month. And youd have done it paying barely half of the normal payment, because of how much of the payment goes to interest early on.This is how even relatively small prepayments can have moderately large impacts on accelerating the repayment of a loan. In disclaimer, a loan that is a lower interest rate, or a shorter term, would see less benefit within the loan. For example, a five-year 10,000 loan would have only about 25 of the first months payment going toward interest.  <response>: That payment formula just gave me a flashback to school haha.Good write up though. Its sad that this isnt common knowledge. 