## Calculating Annual Percentage Rates

This calculator can be used to estimate the annual percentage rate (APR) charged on a loan. The calculator requires a total of five inputs, including:

- The loan value, which is the amount of money borrowed from the lender
- The annual interest rate charged on the loan. Also known as a finance charge, this is the rate of interest charged on the loan’s outstanding principal
- The term of the loan, which is the timeframe over which the loan will be repaid, stated in years
- The total of all application fees paid on the loan, these are sometimes referred to as processing fees or loan origination fees
- Any other cost or fee associated with the loan

The calculator then provides the user with four outputs:

- The monthly payment associated with the interest rate on the loan. This is the amount of money owed the lender each month to pay off the loan in over the specified term
- The effective monthly payment, which considers both the money borrowed as well as the fees associated with the loan
- The total of all fees associated with the loan, which is the sum of the application fees and other fees
- The calculated annual percentage rate (APR) on the loan, which considers both the rate of interest charged as well as all fees

### Annual percentage rates

Perhaps the single most important factor to consider when comparing loans is the published annual percentage rate, which is more commonly displayed as APR. In the United States, the Truth in Lending Act requires all financial institutions to provide consumers with this value on car loans, mortgages, as well as personal loans. The benefit of publishing this rate is the borrower can make fair comparisons between loans since the APR reflects not only the interest rate on the loan but also all fees.

#### Comparing the APR on loans

It’s important to understand APR is function of both the interest rate charged on the loan and the associated fees. If a loan is offered with no fees, then the APR would be the same as the interest rate on the loan. What makes the APR so useful is that a borrower can quickly determine which loan is less costly. For example, a personal loan of 10,000 with a term of five years, no fees, and an interest rate of 5.500% would have an APR of 5.500%. An alternative offering at 5.250% and 75 in fees would have an APR of 5.559%. So, while the borrower might be tempted to choose the loan with the lower interest rate, which would also have a lower monthly payment, the loan with the lower APR is less costly over the five-year term.

### Critical APR assumption

One of the important assumptions we make when calculating APR is that any associated fees will be spread over the course of the loan. As is the case when paying points on a mortgage, an upfront fee may be paid to obtain a lower interest rate. If the loan is paid off early, the advantage of paying the upfront fee is lost. This is an extreme example, but it demonstrates this point. Let’s say a borrower takes out a three-year personal loan for 5,000 at 5.250% and pays fees of 75. If they pay off the loan after only one month, they would have effectively (in terms of APR) paid well in excess of 20% on the loan.