Interest rate calculator
Sometimes you know the payment but not the rate. Enter the loan amount, the regular payment and the number of payments, or for savings the starting balance, regular deposit and end balance. The calculator finds the rate that fits and the effective yearly rate.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Pick loan or savings.
- Enter the amount (or starting balance), the regular payment or deposit and the number of payments.
- For savings, also enter the balance you end up with.
How it works
- Loan: amount = payment × (1 − (1 + i)^−n) ÷ i, solved for the rate per period i by bisection.
- Savings: end = start × (1 + i)^n + deposit × ((1 + i)^n − 1) ÷ i, with deposits at the end of each period.
- Nominal annual rate = i × payments per year; effective = (1 + i)^payments per year − 1.
Worked example
A loan of 200,000 repaid with 360 monthly payments of 1,199.10 has a rate of 6.00% a year (0.5% a month), which is 6.17% effective. Doubling 10,000 in 120 monthly periods with no deposits needs 6.95% a year.
Tips
- Use the payment exactly as the lender states it, rounded or not.
- Payments made at the start of each period are not modelled.
- Results are estimates, not financial advice.
Frequently asked questions
How is the rate found?
There is no closed formula for the rate, so the tool searches numerically: bisection on the annuity equation amount = payment × (1 − (1 + i)^−n) ÷ i until the rate per period is exact to many digits. For savings it uses the future value equation instead.
What is the difference between nominal and effective rate?
The nominal annual rate is the rate per period times the periods per year. The effective annual rate compounds it: (1 + i)^m − 1. A 12% nominal rate paid monthly is about 12.68% effective.
Why does it say the payments are too low?
If the payments add up to less than the amount borrowed, the rate would be negative. Check the amount, the payment and the number of payments.
Does it include fees?
No. Fees, insurance and payment timing differ between lenders. A loan with fees has a higher true cost than the rate shown here.
Is this financial advice?
No. It is a calculation from your inputs; compare it with the rate your lender states.