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Interest Rate Calculator

Find the interest rate on a loan from the loan amount, term, and monthly payment. See the APR, total payments, total interest, and a full amortization schedule.

$
$

Interest Rate (APR)

5.065%

Monthly Interest Rate
0.4221%
Total of Payments
$34,560.00
Total Interest
$2,560.00

Principal vs interest

Principal 93%, Interest 7%
  • Principal93%
  • Interest7%

Amortization schedule

PeriodInterestPrincipalBalance
Year 1$1,387.67$10,132.33$21,867.67
Year 2$862.41$10,657.59$11,210.08
Year 3$309.92$11,210.08$0.00
Interest Rate (APR)5.065%View results

Already know your loan amount, term, and monthly payment, but not the rate? Enter those three and this calculator solves for the annual interest rate (APR), then shows the total of all payments, the total interest, and a full amortization schedule for the rate it found.

Formula

The loan amount is the present value of the stream of level payments. For a monthly rate r over n months and a payment PMT:

Loan = PMT × (1 − (1 + r)^−n) / r

There's no way to rearrange this for r, so the rate is found by numerical search (bisection): try a rate, see whether it reproduces the loan amount, and narrow in. The annual rate is then:

APR = r × 12
The total of payments is simply PMT × n, and the total interest is that total minus the loan amount — independent of the exact rate.

Worked example

InputValue
Loan amount$32,000
Term36 months
Monthly payment$960
Monthly rate (solved)≈ 0.422%
Annual rate (APR)≈ 5.065%
Total of 36 payments$34,560.00
Total interest$2,560.00

Examples

$32,000 loan, $960/month for 3 years

Repaying a $32,000 loan with 36 payments of $960 means paying back $34,560 in total — $2,560 of it interest. The rate that produces a $960 payment on $32,000 over 36 months is about 5.065% APR (a monthly rate of about 0.422%).

Frequently asked questions

How do you find the interest rate on a loan?
Work backward from the payment. The loan amount equals the monthly payment times the present-value annuity factor for the term, so for a known loan amount, term, and payment there is exactly one monthly rate that fits. It has no algebraic solution, so it's found numerically; the annual rate (APR) is that monthly rate times 12.
What is the difference between the interest rate and the APR here?
This calculator reports the nominal annual rate — the monthly rate times 12 — which is how loan rates are normally quoted. A true APR can be slightly higher because it also folds in fees; with no fees the two are the same.
Why do I need the loan amount, term, and payment?
Those three pin down the rate. Given how much you borrowed, how long you'll pay, and how much each payment is, only one interest rate makes the numbers balance. Change any one of them and the implied rate changes.
What if my payments don't add up to more than the loan?
Then no positive interest rate can fit — you'd be repaying less than you borrowed. The total of all payments must exceed the loan amount, and the gap between them is the total interest.

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