# APR Calculator

Calculate the annual percentage rate using our APR calculator.

$% years$
$(paid separately) ## Results: ### Annual Percentage Rate (APR) %  Monthly Payment:$ Amount Financed: $Total Payments:$ Total Finance Charges: $Total Interest:$ Total Fees: $Learn how we calculated this below ## On this page: ## How to Calculate the Annual Percentage Rate The annual percentage rate (APR) is the simple interest rate combined with other fees that the bank may charge you, such as financing fees and prepaid fees. It represents the true cost of borrowing money if a loan is a simple interest loan. If you are taking out a loan with a relatively high interest rate but low fees, you may end up with a lower APR than a loan with a low interest rate but high fees. This is why it is recommended to compare the APR between two financial institutions as opposed to comparing only the interest rates. The APR calculator or the APR formula below provides an easy way to do this. ### APR Formula You can use the following formula to calculate an annual percentage rate. APR = \left ( \frac{ \frac{ \text{fees}\ +\ \text{interest} }{ \text{principal} } }{ n } \right ) \times 365 Where: fees = total fees paid on the loan interest = total interest paid principal = initial loan amount n = loan term in days Note that the calculator uses the Newton-Raphson method for calculating APR, and it accounts for regular interest payments, so the APR results will differ between the APR formula and the APR calculator. For example, let’s assume that you are taking out a$5,000 loan that has a 6% interest rate for 2 years. The bank has already notified you that the financing fees will be $200. What will the APR be on this loan? Before we can use the APR formula above, we should first find what the total interest paid is. We will need to use our simple interest formula below to calculate the total interest. i = PV × r × t where: i = interest PV = present value r = interest rate t = number of periods i = \$5,000 × 0.06 (6\%) × 2
i = \$600 Now that we have the total interest, we have everything we need to find the APR: APR = \left ( \frac{ \frac{ \$200\ +\ \$600 }{ \$5,000 } }{ 730 } \right ) \times 365
APR = \left ( \frac{ \frac{ \$800 }{ \$5,000 } }{ 730 } \right ) \times 365
APR = \left ( \frac{ 0.16 }{ 730 } \right ) \times 365
APR = 8\%

When shopping for different loans, it is recommended that you compare the APR between them instead of just the interest rate because the APR represents the true cost of borrowing on a loan.

Let’s look at the following examples to see how we might compare two loans.

You are looking for a $10,000 auto loan for 4 years. Bank A has quoted you a 5% loan with$100 in financing fees, whereas Bank B is willing to offer you a 4% loan but with $600 in financing fees. How can you know which loan would be a better option? We need to compare the APR for both and see which offers a lower APR. But, again, we first need to calculate the simple total interest so we can plug them into the APR formula. Interest for Bank A: i = \$10,000 × 0.05 (5\%) × 4
i = \$2,000 Interest for Bank B: i = \$10,000 × 0.04 (4\%) × 4
i = \$1,600 Now that we know the total interest, let’s calculate the APR for each loan. APR for Bank A: APR = \left ( \frac{ \frac{ \$100\ +\ \$2,000 }{ \$10,000 } }{ 1,460 } \right ) \times 365
APR = \left ( \frac{ \frac{ \$2,100 }{ \$10,000 } }{ 1,460 } \right ) \times 365
APR = \left ( \frac{ 0.21 }{ 1,460 } \right ) \times 365
APR = 5.25\%

APR for Bank B:

## APR vs. APY

APY stands for Annual Percentage Yield. APY is the interest rate that is calculated once compounding is taken into effect. Since this is a compounding interest rate, the more frequent the compounding, the higher the total interest will be.

While interest can technically be compounded at any time frequency, the most common frequencies are daily, monthly, quarterly, semiannually, and annually. These are also the available options in our APY calculator.

So, they are similar in that they both annualize the interest rate (and why they both have “annual” in their names).

However, APR and APY differ in several ways:

• The APY takes compounding into consideration, but the APR does not. So the APR more accurately represents the cost of borrowing on a loan because most loans use simple interest. The APY more accurately represents what the return on investment is for a savings account because the bank will pay you compound interest (interest on the principal balance and previously accrued interest).
• The APR includes additional fees that the financial institution may charge on top of the interest rate, whereas the APY only includes the interest rate.

Our APR to APY calculator shows the comparison from the compound to simple interest rate.

You can also use our interest calculator to compare the total interest between simple interest and compound interest.