Finance / Interest
Interest Rate Calculator: Loan Payments, Growth and APR/APY
Find the interest rate implied by a loan amount, monthly payment and term, or by present and future values. Convert between nominal yearly rates and effective yearly rates.
Interest Rate Calculator: Loan Payments, Growth and APR/APY: Loan mode solves the equal-payment amortisation equation for a non-negative nominal annual rate up to 100%, with 1 to 1,200 end-of-month payments. Present/future value mode solves a constant growth rate without extra cash flows. APR/APY conversion accounts for compounding. The displayed nominal loan rate excludes fees and is not a lender’s regulated fee-inclusive APR. Runs 100% locally in your browser with zero server file uploads.
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Monthly rate: 1%. Payment checked at this rate: 88.84878868. Total interest: 66.18546416.
- At zero interest, the payment is loan amount ÷ number of payments = 83.33333333.
- Find r in payment = P × r / (1 − (1 + r)^−n), using monthly r and end-of-month payments.
- Test rates between 0% and 100% nominal yearly interest, narrowing the interval until the calculated payment matches.
- Nominal annual rate = 12 × monthly rate. Effective annual rate = (1 + monthly rate)^12 − 1.
Loan mode assumes equal monthly payments at the end of each month, no fees and no balloon balance. The nominal rate is not a lender's fee-inclusive APR. Present/future value mode assumes no added deposits or withdrawals.
Equal-payment loans
OpenStax presents the annuity and amortisation relationships (https://openstax.org/books/principles-finance/pages/8-2-analyze-the-relationship-between-annuity-payments-and-present-values). For monthly rate r and n payments, payment = principal × r / (1 − (1 + r)^−n).
Nominal rates and fees
The CFPB distinguishes interest rates from fee-inclusive loan APR (https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-loan-interest-rate-and-the-apr-en-733/). This calculator reports a nominal rate without fees. APY = (1 + APR/m)^m − 1 for m equal compounding periods per year, with decimal rates.
How to use it
- Choose loan payments, present/future values or APR/APY conversion.
- Enter the known amounts and term, or the rate and compounding frequency.
- Read the implied nominal and effective annual rates and their working steps.
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Frequently asked questions
What happens if payments are too low?
If the total of the scheduled payments is below the amount borrowed, no non-negative rate can repay the loan under these assumptions. The calculator explains this instead of returning a rate.
Does this include fees in APR?
No. The nominal annual rate here is twelve times the monthly interest rate. A lender’s disclosed APR can include fees and follow jurisdiction-specific rules.
Can present/future value mode return a negative rate?
Yes. A positive future value below the positive present value implies a negative growth rate, assuming no added deposits or withdrawals.
Why are APR and APY different?
Compounding makes the effective annual rate differ from the nominal annual rate. At 12% nominal with monthly compounding, APY is (1.01^12 − 1) × 100, approximately 12.6825%.
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