what is compounding 
compounding is the process in which an asset s earnings from either capital gains or interest are reinvested to generate additional earnings over time this growth calculated using exponential functions occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods compounding therefore differs from linear growth where only the principal earns interest each period sydney saporito investopediaunderstanding compoundingcompounding typically refers to the increasing value of an asset due to the interest earned on both a principal and an accumulated interest this phenomenon which is a direct realization of the time value of money tmv concept is also known as compound interest compounding is crucial in finance and the gains attributable to its effects are the motivation behind many investing strategies for example many corporations offer dividend reinvestment plans drips that allow investors to reinvest their cash dividends to purchase additional shares of stock reinvesting in more of these dividend paying shares compounds investor returns because the increased number of shares will consistently increase future income from dividend payouts assuming steady dividends investing in dividend growth stocks on top of reinvesting dividends adds another layer of compounding to this strategy that some investors refer to as double compounding in this case not only are dividends being reinvested to buy more shares but these dividend growth stocks are also increasing their per share payouts formula for compound interestthe formula for the future value fv of a current asset relies on the concept of compound interest it takes into account the present value of an asset the annual interest rate the frequency of compounding or the number of compounding periods per year and the total number of years the generalized formula for compound interest is 1f v p v 1 i n n t where f v future value p v present value i annual interest rate n number of compounding periods per time period t the time period begin aligned fv pv times big 1 frac i n big nt textbf where fv text future value pv text present value i text annual interest rate n text number of compounding periods per time period t text the time period end aligned fv pv 1 ni ntwhere fv future valuepv present valuei annual interest raten number of compounding periods per time periodt the time period this formula assumes that no additional changes outside of interest are made to the original principal balance curious what 100 daily compounding looks like one grain of rice the folk tale by demi is centered around a reward where a single grain of rice is awarded on the first day and the number of grains of rice awarded each day is doubled over 30 days at the end of the month over 536 million grains of rice would be awarded on the last day 2increased compounding periodsthe effects of compounding strengthen as the frequency of compounding increases assume a one year time period the more compounding periods throughout this one year the higher the future value of the investment naturally two compounding periods per year are better than one and four compounding periods per year are better than two to illustrate this effect consider the following example given the above formula assume that an investment of 1 million earns 20 per year the resulting future value based on a varying number of compounding periods is as evident the future value increases by a smaller margin even as the number of compounding periods per year increases significantly the frequency of compounding over a set length of time has a limited effect on an investment s growth this limit based on calculus is known as continuous compounding and can be calculated using the formula 3f v p e r t where e irrational number 2 7183 r interest rate t time begin aligned fv p times e rt textbf where e text irrational number 2 7183 r text interest rate t text time end aligned fv p ertwhere e irrational number 2 7183r interest ratet time in the above example the future value with continuous compounding equals fv 1 000 000 2 7183 0 2 x 1 1 221 404 compounding is an example of the snowball effect where a situation of small significance builds upon itself into a larger more serious state compounding on investments and debtcompound interest works on both assets and liabilities while compounding boosts the value of an asset more rapidly it can also increase the amount of money owed on a loan as interest accumulates on the unpaid principal and previous interest charges even if you make loan payments compounding interest may result in the amount of money you owe being greater in future periods the concept of compounding is especially problematic for credit card balances not only is the interest rate on credit card debt high but the interest charges also may be added to the principal balance and incur interest assessments on itself in the future for this reason the concept of compounding is not necessarily good or bad the effects of compounding may work for or against an investor depending on their specific financial situation example of compoundingto illustrate how compounding works suppose 10 000 is held in an account that pays 5 interest annually after the first year or compounding period the total in the account has risen to 10 500 a simple reflection of 500 in interest being added to the 10 000 principal in year two the account realizes 5 growth on both the original principal and the 500 of first year interest resulting in a second year gain of 525 and a balance of 11 025 after 10 years assuming no withdrawals and a steady 5 interest rate the account would grow to 16 288 95 without having added or removed anything from our principal balance except for interest the impact of compounding has increased the change in balance from 500 in period 1 to 775 66 in period 10 in addition without having added new investments on our own our investment has grown 6 288 95 in 10 years had the investment only paid simple interest 5 on the original investment only annual interest would have only been 5 000 500 per year for 10 years 