How to use this calculator
- Enter or choose amount borrowed.
- Enter or choose monthly payment.
- Enter or choose number of monthly payments.
- The annual interest rate updates as you type. Use Copy result or Share to keep it.
Method
Find i such that Payment = L × i(1+i)^n ÷ ((1+i)^n − 1) (solved numerically by bisection); Annual rate = 12 × i; Effective rate = (1 + i)^12 − 1
- L
- amount borrowed
- n
- number of monthly payments
- i
- monthly interest rate
Worked example
- Total repaid = 483.32 × 60 = $28,999.20, so interest = $3,999.20.
- At i = 0.5% a month, 25,000 × 0.005 × 1.005^60 ÷ (1.005^60 − 1) = 483.32, matching the payment.
- Annual rate = 12 × 0.5% = 6%; effective rate = 1.005^12 − 1 = 6.1678%.
Borrowing $25,000 and repaying $483.32 a month for 60 months means a 6% annual interest rate.
What the result means
If a lender quotes a lower rate than this calculator finds for the same payment, fees or add-ons have been folded into the payment. The effective rate is useful when comparing with savings rates.
Assumptions and limits
- Payments are equal, monthly and start one month after the loan is made.
- The amount borrowed is what you actually receive; fees deducted upfront raise the true rate.
- This is the rate implied by the payments, not a regulatory APR, which may include specific fees under local rules.
Questions
Why is there no simple formula for the rate?
The payment formula cannot be rearranged for the rate, so it is found by trying rates until the payment matches, as financial calculators do.
What if the payments add up to exactly what I borrowed?
Then the rate is 0%. If they add up to less, no positive rate fits.
Please note: This calculator gives estimates for planning. It is not financial advice, and lenders’ actual terms, fees and rounding may differ.