## APR to APY conversion

By now, you must have noted that banks and other financial institutions advertise their financial products with quoted APY when they are talking about CDs (certificate of deposit) and savings accounts and the mortgage and loan related products are advertised with quoted APR.

The main difference between the **annual percentage rate** and **annual percentage yield** is that the APR does not consider compounding, while the APY does. Compound means that the interest is added to the principal, and from that moment, not only the base principal, but the added interest earns interest as well.

Because of this, APR is naturally lower and APY is naturally higher. Since everybody wants higher interest rate on savings and lower interest rate on loans, this is why certificate of deposit and savings account related financial products mainly advertise annual percentage yield and mortgage or loan related products advertise annual percentage rate.

Let us compare two savings account offers. The first offer quotes a nominal interest rate of 6.00 percent and pays interest monthly, while the other one quotes 6.10 percent of annual percentage yield. If we enter these values into the **apy calculator** on the left, we will notice, that the 6.00 percent offer equals to 6.16778 percent APY. We know that there is no significant difference between the two offers, and almost every time the financial institutions will quote APY instead of APR, but still, the lower annual interest rate gave us a higher income return on an investment.

APR is the periodic interest rate multiplied by the number of periods in a year. The annual percentage rate for 1.50 percent monthly interest rate will be 1.50 * 12 = 18.00 percent.

APY considers compounding. To calculate APY, first we have to add 1 to the periodic interest rate (e.g. 1.015 if the monthly rate is 1.50 percent), then raise this sum to the number of periods in a year (this will be 12 in our case) and finally subtract 1 from the result.

In numbers: 18.00 percent nominal interest rate is 1.50 percent monthly interest rate, which is 0.015 (1.50 / 100); 0.015 + 1 equals 1.015; monthly compounding means, that we have 12 periods in a year, so we will have (1.015)^12, that equals 1.1956182; we subtract 1 from this to get 0.1956182, what is equal to 19.56182 percent.