what apy can tell you
any investment is ultimately judged by its rate of return whether it s a certificate of deposit cd a share of stock or a government bond the rate of return is simply the percentage of growth in an investment over a specific period of time usually one year however rates of return can be difficult to compare across different investments if they have different compounding periods one may compound daily while another compounds quarterly or biannually comparing rates of return by simply stating the percentage value of each over one year gives an inaccurate result as it ignores the effects of compounding interest it is critical to know how often that compounding occurs since the more often a deposit compounds the faster the investment grows this is due to the fact that every time it compounds the interest earned over that period is added to the principal balance and future interest payments are calculated on that larger principal amount suppose you are considering whether to invest in a one year zero coupon bond that pays 6 upon maturity or a high yield money market account that also pays a 6 rate but with monthly compounding at first glance the yields appear equal because since they are both stated as 6 but when the effects of compounding are included the money market investment actually yields a higher apy 1 005 12 1 0 06168 6 17 apy comparing two investments by their simple interest rates doesn t work as it ignores the effects of compounding interest and how often that compounding occurs apy vs aprapy is similar to the annual percentage rate apr used for loans the apr reflects the effective percentage that the borrower will pay over a year in interest and fees for the loan apy and apr are both standardized measures of interest rates expressed as an annualized percentage rate however apy takes into account compound interest while apr does not furthermore the equation for apy does not incorporate account fees only compounding periods that s an important consideration for an investor who must consider any fees that will be subtracted from an investment s overall return example of apyif you deposited 100 for one year at 5 interest and your deposit was compounded quarterly at the end of the year you would have 105 09 if you had been paid simple interest you would have had 105 the apy would be 1 05 4 4 1 05095 5 095 begin aligned text the apy would be bigg 1 frac 05 4 bigg 4 1 05095 5 095 end aligned the apy would be 1 4 05 4 1 05095 5 095 it pays 5 a year interest compounded quarterly and that adds up to 5 095 that s not too dramatic however if you left that 100 for four years and it was being compounded quarterly your initial deposit would have grown to 121 99 without compounding it would have been 120 x d 1 r n n y 100 1 05 4 16 100 1 21989 121 99 where x final amount d initial deposit r nominal rate n number of compounding periods per year y number of years begin aligned x d bigg 1 frac r n bigg ny 100 bigg 1 frac 05 4 bigg 16 100 1 21989 121 99 textbf where x text final amount d text initial deposit r text nominal rate n text number of compounding periods per year y text number of years end aligned x d 1 nr ny 100 1 4 05 16 100 1 21989 121 99where x final amountd initial depositr nominal raten number of compounding periods per yeary number of years 