Basic APR Calculator

Basic Calculator

Calculators

Financial

Interest & APR

Basic APR Calculator

Loan Amount: $

Interest Rate: %

Term in Months: #

Financing Fees: $
To be added to the loan

Answer:

Annual Percentage Rate

APR:

Original Loan Amount:

Interest:

Financing Fees:

Total Financing Charges:

Total Loan Principal:

Total Payments:

Monthly Payment:

How could this calculator be better?

Get a Widget for this Calculator

Calculator Use

This basic APR Calculator finds the effective annual percentage rate (APR) for a loan such as a mortgage, car loan, or any fixed rate loan. The APR is the stated interest rate of the loan averaged over 12 months.

Input your loan amount, interest rate, loan term, and financing fees to find the APR for the loan. You can also create an amortization schedule for your loan principal plus interest payments.

See the Advanced APR Calculator for APR calculations that include interest compounding and payment frequency options.

Loan Amount: The original principal on a new loan or remaining principal on a current loan.
Interest Rate: The annual interest rate or stated rate on the loan.
Term: The number of months (number of payments) required to repay the loan.
Financing Fees: The sum of all additional costs involved in the loan transaction including points, fees, closing costs, processing fees, etc. This does not include interest paid over the course of the loan.
Total Financing Charges: The sum of all financing fees plus all interest paid over the course of the loan; the total cost of having the loan.
Total Loan Principal: The total amount financed, including original principal loan amount plus financing fees rolled into the loan.
Total Payments: The sum of total loan principal plus total financing charges.

APR Calculations

This calculator determines the APR of a loan with additional fees or points rolled into the amount borrowed.

We calculate 1) the monthly payment based on the actual loan amount then 2) back-calculate to a new interest rate - which is the APR - as if this payment was made on just the amount financed.

What is APR?

APR represents the average yearly cost of a loan over the term of the loan. This cost includes financing charges and any fees or additional charges associated with the loan such as closing costs or points. (Some fees are not considered "financing charges" so you should check with your lending institution.)

If you take a mortgage for $100,000 at an interest rate i with no additional fees then i is likely your APR. However, if you have additional fees rolled into the loan, your APR will be higher than the stated interest rate i.

APR Basic Example

Suppose you lend me $20 for a year at 10% interest. At the end of the year I will owe you 20 + (20 x 10%) = 20 + 2 = $22. Now, 2/20 = 0.10, so the APR is 10%. This is a one-year loan at an interest rate of 10% and an APR of 10%.

Now suppose you lend me $20 for a year at 10% interest, but you are also charging me a $3 fee. And I can pay you the fee at the end of the year. At the end of the year I will owe you 20 + (20 x 10%) + 3 = 20 + 2 + 3 = $25. Now, 5/20 = 0.25, so the APR is 25%. This is a one-year loan at an interest rate of 10% and an APR of 25%.

How to Calculate APR for a Loan

Suppose you are purchasing a car for $15,000 and financing the purchase at 5% for 5 years (60 months) and you will pay a $200 financing fee rolled into the loan.

The principal, or present value (PV) of the loan is $15,000 + $200 = $15,200. Interest compounds monthly and the periodic inerest rate i is the interest rate per month in decimal form. 5% as a decimal is 0.05 per year. 0.05/12 = 0.00417 per month. The number of months n is 60.

Solve the following equation to calculate the monthly payment

$ PMT=\dfrac{PVi(1+i)^n}{(1+i)^n-1} $

$ PMT=\dfrac{15,200(0.00417)(1+0.00417)^{60}}{(1+0.00417)^{60}-1}=286.84 $

Since you really only received $15,000 and are making a payment on a greater loan amount, in reality you are paying what amounts to a higher interest rate. You are paying $286.84 per month for the $15,000 you received, not the total $15,200. Putting these values into the equation:

$ 286.84=\dfrac{15,000i(1+i)^{60}}{(1+i)^{60}-1} $

From here you would need to solve the equation for i and calculate i. Multiplying i x 12 gives you the APR = 5.547%.

You can use the Loan Calculator to calculate the APR = 5.547%

This is this example using this APR Calculator

The calculation for i is not shown here because finding the interest rate is a complex calculation involving the Newton-Raphson Method which you can read about at MathWorld. Essentially, you keep making guesses for the value of i until the equation above becomes true.