# How Annual Percentage Yield Works

Annual percentage yield, or APY, is often used to quote to investors on interest-bearing investment products as the effective rate of return. The effective yield is calculated based on the periodic rate for periodic interest payments within any given year by way of compounding. The conventionally stated annual interest rate is used to arrive at the periodic rate, divided by the number of compounding periods in the year and is never the real rate of return unless interests compound on a yearly basis only. Therefore, annual percentage yield is always higher than or at least equal to the nominal annual interest rate.

The Power of Compounding

Compounding is to earn additional interest on earlier interest besides principle. For example, if an investment product pays interest semi-annually, it would compound interest twice a year. For a 10% annual interest rate, the periodic compounding rate would be 5%, dividing the annual rate of 10% by 2. Thus interest earned at the half-year point would be $5 for every $100 in principle. Now the principle for the second period would be $105 after adding the $5 interest to the initial $100 principle and the interest for the second period would be $5.25, multiplying the new principle of $105 by the periodic rate of 5%. As a result of the compounding, total interests for the year would be $10.25, adding the $5 from the first period and $5.25 from the second period. On the another hand, the nominal interest earned on every $100 would have been only $10 at the end of the year because of no compounding. So the effective or real rate of return for investors on a semi-annually compounded investment product with a stated annual interest rate of 10% is a 10.25% of annual percentage yield. To calculate APY on more frequent compounding, like quarterly, monthly, or maybe even daily compounded investment, a financial calculator can do the math better.

APY for Investors

Without APY as the yardstick, it makes it harder for investors to compare different investment products that would have been quoted in nominal annual interest rates. Actual returns are affected by not only the interest rate but also how often compounding occurs. For two investment products with the same stated annual interest rate, the one that compounds monthly earns higher returns for investors than the one that compounds only semi-annually. Also, the power of compounding can sometimes make investment products with lower stated interest rates better choices than those that have higher stated interest rates. For example, investment with a 11.5% interest rate when compounded monthly would yield an actual return of more than 12%, surpassing one that has a stated 12% interest rate but compounds only annually.

APY for Issuers

Financial institutions offering investment products prefer to quote their earning rate in the form of APY. It seems that the word yield in APY has everything to do with earning returns from an investment product, but that’s not in the least why APY often associates with investment products in rate quotes. To entice investors to buy their investment products, financial institutions would most likely to quote APY because it’s the highest rate possible.

The same APY is also the amount of interests a borrower must pay if the transaction is lending to borrowers, instead of investing by investors, but APY is never quoted. In a lending situation, the annual interest rate or annual percentage rate (APR) in many cases(see explanation in the next section) is quoted to borrowers, simply because it’s a lower number comparing to APY, as people would be looking for the lowest rate possible when they borrow.

Annual Interest Rate vs. Annual Percentage of Rate

The term annual percentage rate would be used when, in lending, transaction costs or borrowing fees are involved and subtracted from the total borrowing amount. Interest rate is only a reflection of the time value of money on borrowed capital and does not take into account any fees that are in addition to interests and paid to secure a borrowing. Such fees increase the true borrowing cost. Suppose one borrows $100 with an annual interest rate of 5%, but the lender requires that in order to get the loan, a transaction fee of $10 is to be assessed. So the actual amount of money obtained from the $100 loan is only $90, but the annual interest would still be 5% on $100, which is $5. Thus effectively, one pays $5 interest on an amount of $90 actually obtained and that is a rate of 5.56%. Borrowing cost with fee considerations is referred as annual percentage rate, or APR, replacing nominal interest rate for the purpose of compounding to further arrive at the effective or real borrowing cost, the APY.

With APR, loans with different fee structures can be compared on the same basis. Although like any nominal interest rate, APR does not take into account any compounding effect, according to the Truth in Lending Act of 1968, APR is the rate that lenders must least provide to borrowers alongside the interest rate of the loan. Similar to why APY is used in investing, APR is used in borrowing not least because the word rate in APR seems to have everything to do with paying interests on a loan; but because lenders would not want to quote the real rate of APY, which is always higher than APR.