How to find the interest rate of a loan
Lenders, dealers and stores often tell you the monthly payment but not the interest rate. If you know how much you borrow, for how long and what you pay each month, this interest rate calculator works out the yearly interest rate you are really paying, so you can compare the offer with others.
The formula behind the rate
A fixed-rate loan is repaid in equal monthly payments:
M = P × r × (1 + r)n / ((1 + r)n − 1)
- M is the monthly payment, P the loan amount, n the number of months and r the monthly rate.
- The formula cannot be solved for r directly, so the calculator tries rates until the payment matches yours to the cent, the same way a financial calculator does.
- The interest rate shown is r × 12, the yearly rate compounded monthly that loans quote.
- The effective annual rate, (1 + r)12 − 1, is slightly higher because the interest compounds every month.
Example
You borrow $32,000 and pay $960 a month for 3 years. You pay $34,560 in total, so $2,560 is interest, and the interest rate is 5.065%, or an effective 5.184% a year. If the same payments ran for 41 months instead of 36, the rate would be 12.308%: five extra payments more than double it.
Interest rate by monthly payment
A $32,000 loan repaid over 60 months:
| Monthly payment | Total interest | Interest rate |
|---|---|---|
| $560 | $1,600 | 1.937% |
| $580 | $2,800 | 3.351% |
| $600 | $4,000 | 4.735% |
| $620 | $5,200 | 6.091% |
| $650 | $7,000 | 8.075% |
| $700 | $10,000 | 11.265% |
Every extra $20 a month on this loan adds roughly 1.4 percentage points to the rate.
Fees raise the real rate
If the lender keeps a fee out of the loan, you pay interest on money you never get. On the example loan, a $1,000 fee means you receive $31,000 but still pay $960 a month: enter $31,000 as the loan amount and the real rate, the APR, is 7.198% instead of 5.065%. The APR calculator works this out with the fees entered separately.
Add-on interest: a rate that is not what it seems
Some dealers and small lenders quote add-on interest: the rate is charged on the full amount for the whole term, even though you pay the loan down every month. A 4% add-on rate on $32,000 for 3 years adds $3,840 of interest, so the payment is $995.56. Enter that payment in the calculator and the real interest rate is 7.511%, almost twice the quoted rate.
Things to keep in mind
- A low monthly payment over a long term can hide a high rate. Always compare the rate and the total you pay.
- For credit cards and loans with changing rates, the result is only an average; the credit card calculator handles a card balance.
- To see the payment for a rate you already know, use the loan calculator or the payment calculator; for a car with tax and a trade-in, the auto loan calculator.
- For savings, where you know the start and end amounts, the finance calculator finds the rate with its I/Y key.