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APR Calculator
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This calculator first calculates the monthly payment using C+E and the original interest rate r = R/1200:
The APR (a = A/1200) is then calculated iteratively by solving the following equation using the Newton-Raphson method:
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| APR Definition |
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Annual Percentage Rate (APR) is the equivalent interest rate considering all the added cost to a given loan. Naturally, it is a
function of the loan amount, the interest rate, the total added cost, and the terms. The APR would equal the interest rate if there is no
additional cost to a given loan. Here is an example:
Total money borrowed:
(The actual amount of money you are going to receive from the lender.) |
$200,000 |
Total extra cost:
(Points, application fee, closing fee, title fee,..., everything.) |
$5,000 |
| Interest rate: |
7.5% |
| Term: |
30 years |
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To find the monthly payment for this loan, we can use the
Loan Calculator Scenario #1 with $205,000 as the total loan amount
(you are not borrowing this much but you will owe this amount when the loan is closed),
7.5% as the interest rate, and 360 as the number of payments (1 payment/month for 30 years).
The monthly payment is found to be $1,433.39.
Now, since you are only borrowing $200,000 but paying $1433.39/month for 30 years,
we can back-calculate the equivalent interest rate (APR) by using the
Loan Calculator Scenario #2. The answer is,
Annual Percentage Rate = 7.75%.
The APR Calculator on this page will perform these two calculations in one
pass.
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