Interest Rate Calculator
Give the calculator any three of the loan amount, the monthly payment, the number of months and the annual interest rate, and it finds the fourth. It is the way to work out the rate of a loan when you only know the payment, for example a car loan or a store financing offer. It also shows the total paid, the total interest and the effective yearly rate. Everything runs in your browser.
60 months is 5 years
Check: $20,000.00 at 6.0004% over 60 months gives a payment of $386.66.
A loan with fixed monthly payments follows one formula: the payment equals the loan times the monthly rate, divided by one minus (1 plus the monthly rate) to the power of minus the number of months. Given any three of the loan, the payment, the number of months and the annual rate, the fourth can be found. The rate has no closed form, so the calculator searches for it until the payment matches. If the payments add up to exactly the loan, the rate is zero, and if they add up to less, no rate can work. The rate shown is the nominal annual rate with monthly compounding, which is how loan quotes are usually stated, and the effective yearly rate is shown next to it. Fees are not included, so the rate you find from a payment that includes them will be higher than the quoted rate. Everything is worked out in your browser.
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A loan with equal monthly payments follows one formula: the payment equals the loan times the monthly rate, divided by one minus (1 plus the monthly rate) to the power of minus the number of months. The payment, the term and the loan have direct solutions, but the rate does not, because it sits inside a power. The calculator finds it by bisection: it tries rates until the payment matches. For a 20,000 loan repaid with 386.66 a month over 60 months the rate is 6.00%, and the total interest is about 3,200. If the payments add up to exactly the loan, the rate is zero, and if they add up to less, no rate can produce them. The number of months comes from the closed form of minus the natural log of 1 minus (loan times the monthly rate over the payment), divided by the natural log of 1 plus the monthly rate, and it fails if the payment does not even cover the first month's interest. The rate is the nominal annual rate with monthly compounding, the usual way loans are quoted, and the effective yearly rate is shown beside it: 6% compounded monthly is 6.1678% a year. If the payment includes fees, insurance or other charges, the rate you find is higher than the lender's quoted rate.
How do I find the interest rate of a loan?▾
You need the loan amount, the monthly payment and the number of months. There is no simple formula for the rate, so the calculator searches for the rate at which that payment repays the loan in that time.
Why is the rate I find higher than the quoted rate?▾
If the payment you used includes fees, insurance or other charges, those costs are counted as interest. Use the payment for principal and interest only to match the quoted rate.
What is the difference between the rate and the effective rate?▾
The nominal rate is the quoted annual rate, compounded monthly. The effective rate, or APY, includes the effect of compounding within the year, so it is a little higher: 6% a year compounded monthly is 6.1678%.
What if my payment does not cover the interest?▾
Then the balance never falls, and the loan is never repaid. The calculator reports this when the payment is not above the first month's interest.
Is my data uploaded?▾
No. The calculation runs in your browser and nothing you enter is sent anywhere.