Interest Rate Calculator
Find the interest rate of a loan from the amount borrowed, the payment and the number of payments.
Result
Annual interest rate: 6.0004%
Assumes level payments with nothing left owing at the end and no fees. A loan with fees has an APR above this rate.
- Rate per payment period
- 0.5%
- Effective annual rate
- 6.1682%
- Total paid
- $23,199.60
- Total interest
- $3,199.60
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Results are arithmetic estimates based on the values you enter. Rates, fees and terms are set by your lender or provider, and your actual agreement controls what you pay or receive. Confirm important figures with them or with a qualified adviser. Read the full disclaimer
How to use the Interest Rate Calculator
- Enter the amount you borrowed, the regular payment and how many payments there are.
- Choose how often the payments fall.
- Read the annual interest rate the payments imply, and the effective rate once interest compounds.
How the rate is found
With an amount borrowed PV, a payment PMT and n payments, the rate per payment i is the one that makes the payments worth exactly what was borrowed:
PV = PMT × (1 − (1 + i)^−n) ÷ iannual rate = i × payments a yearThere is no formula that rearranges this for i, so the page searches for it. It tries a rate, sees whether the payments are worth too much or too little, and halves the gap until the answer is exact to far more places than are shown. The same search runs on the TVM calculator.
The nominal and the effective rate
The annual rate here is the rate per payment times the number of payments a year, the way lenders quote loan rates. The effective annual rate compounds the rate per payment over a year: (1 + i) raised to the number of payments a year, minus one.
What this assumes
Every payment is the same, the first falls one period after the loan starts, nothing is left owing at the end, and there are no fees. A loan with a balloon or a remaining balance can be solved on the TVM calculator, which takes a future value as well.
With your numbers
- Total paid = $386.66 × 60 = $23,199.60, of which $3,199.60 is interest
- The rate per payment i at which $386.66 × (1 − (1 + i)^−60) ÷ i = $20,000.00 is 0.500036%
- Annual interest rate = 0.500036% × 12 = 6.0004%
Quick reference
Assumes level payments with nothing left owing at the end and no fees. A loan with fees has an APR above this rate.
| Example | Annual interest rate |
|---|---|
| 20,000 repaid at 386.66 a month for 60 months | 6.0004% |
| 32,000 repaid at 973.50 a month for 36 months | 5.9999% |
| 250,000 at 1,580.17 a month for 30 years | 6.5% |
| 10,000 repaid at 1,000 a month for 12 months | 35.0742% |
| 12,000 repaid at 1,000 a month for 12 months | 0% |
| 15,000 repaid at 350 biweekly for 50 payments | 16.1755% |
Common questions about the Interest Rate Calculator
- Why is the rate not exactly the one my lender quoted?
- Because a payment is rounded to the cent, and a rounded payment implies a rate a hair away from the quoted one. 60 payments of 386.66 on 20,000 imply 6.0004%, while the unrounded payment at exactly 6% is 386.656. The fourth decimal place is where that rounding shows.
- Is this the APR?
- Only if there are no fees. The APR counts finance charges paid up front, such as origination fees and points, so a loan with fees has an APR above the rate found here. The APR calculator solves that case.
- What is the effective annual rate?
- The rate you pay over a whole year once each month’s interest is charged on the last. A 6% annual rate paid monthly is 0.5% a month, which compounds to about 6.17% over twelve months. Loan rates are quoted as the nominal figure, so compare like with like.
- Why does it refuse my numbers?
- If the payments add up to less than the amount borrowed, the loan would have to charge a negative interest rate to balance, which no loan does. Check the payment and the number of payments.