## APY to APR conversion

Similar to the usage of the APY rate, the lenders, banks and other financial institutions advertise their loan related and mortgage loan related financial products with quoted **annual percentage rate** (APR) rather than **annual percentage yield** (APY), while CDs (certificate of deposit) and savings accounts are advertised with quoted APY.

Since the **annual percentage rate** does not consider compounding, while **annual percentage yield** does, it is natural that the APR will always be lower than the APY (compounding 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). This is why, the loan and mortgage related products are mainly advertised with APR (everybody wants to pay lower interest on the borrowed principal) and certificate of deposit and savings accounts are advertised with APY (everybody wants higher interest rate earnings on their money).

To convert annual percentage yield to annual percentage rate, first we have to know, **what is APR**. The periodic interest rate (e.g. 1.50 percent monthly interest rate) multiplied by the number of periods in a year (e.g. 12 for monthly period frequency) gives us the APR (e.g. 1.50 percent * 12 = 18.00 percent). For this we do not need a special calculator, but to **convert APY to APR**, we need one, since:

**APY = (1 + periodic rate)^(periods in a year) – 1**

and from this, we have to get the periodic rate. If we put the above mentioned numbers in the calculator on the left, we will get 16.66612 percent APR from the 18.00 percent APY, or 18.00 percent APR (1.50 percent monthly interest rate) from 19.56182 percent APY.

## Mortgage APR

**Mortgage loan APR calculation** is slightly different, from the above mentioned. Loan and mortgage loan offers often quote annual interest rate, while they tend to forget to mention origination fee, discount points and other fees in their advertisements. To get the fixed rate **mortgage annual percentage rate**, we have to add these closing costs to the annual interest rate.

The mortgage APR formula is:**L - F = P / (1 + i) + P / (1 + i)^2 +... (P + B) / (1 + i)^n**

where **L** is the mortgage loan amount, **F** are the origination fee, discount points and other fees paid to the lender, **P** is the periodic payment amount, **n** is the last payment period and **B** is the balance in period n. As you can see, the mortgage annual percentage rate calculation is almost impossible without a computer, so feel free to use our **mortgage APR** calculator.

Let us compare two mortgage loan offers. The first offer quotes an interest rate of 3.80 percent and 2 percent origination fee, while the other one quotes 3.65 percent annual interest rate, 2 percent origination fee plus 2 discount points and higher other fees. If we enter these values into the mortgage APR calculator we will notice, that the 3.80 percent offer equals to 3.96280 percent APR and the 3.65 percent offer equals to 3.97120 percent APR. There is no significant difference between these the two offers, but as you can see, a lower interest rate does not necessary mean a cheaper loan.

Note that the APR assumes you will keep the loan for its full term.