Interest Rate Calculator
Find the interest rate on a loan from the amount borrowed, the monthly payment and the number of payments, with the effective annual rate and total interest.
Results
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Quick Answer
When you know the loan amount, payment and term, the interest rate is the rate that makes the payments repay the loan exactly. Borrowing $25,000 and paying $500 a month for 5 years works out to an interest rate of about 7.420% a year. There is no simple formula, so the calculator solves for it by trial.
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Table of Contents
- Interest Rate Calculator
- Quick Answer
- Related Calculators
- How This Interest Rate Calculator Works
- How to Use the Interest Rate Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- Interest Rate vs APR
- Rate for a $10,000 Loan Over 5 Years
- What Affects Your Rate
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Interest Rate Calculator Works
Enter how much you borrowed, your monthly payment and how long you will pay. The calculator tries rate after rate, narrowing in until the standard loan payment formula gives exactly your payment. It then shows the yearly rate, the monthly rate, the effective annual rate and the total interest you will pay.
Quick explanation: a higher payment for the same loan and term means a higher interest rate.
- Annual rate: monthly rate × 12, as most loans quote it.
- Effective annual rate: includes monthly compounding.
- Total interest: all payments minus the amount borrowed.
How to Use the Interest Rate Calculator
- Enter the amount borrowed.
- Enter the monthly payment.
- Enter the term and choose years or months.
- Press Calculate.
- Read the interest rate, effective rate and total interest.
Core Formulas
- Payment: M = P × r ÷ (1 − (1 + r)^−n)
- Solve for r: find the monthly rate r that makes the formula equal your payment
- Annual rate: r × 12
- Effective annual rate: (1 + r)¹² − 1
P is the loan amount, M the monthly payment and n the number of payments.
Key Terms
- Interest rate: the yearly cost of borrowing, as a percent of the balance.
- APR: annual percentage rate, the yearly cost including some fees.
- Effective annual rate: the yearly rate after compounding.
- Amortization: paying a loan off with equal payments over time.
- Principal: the amount borrowed.
Worked Example
A dealer offers a $25,000 car loan at $500 a month for 60 months.
- Total paid = $500 × 60 = $30,000
- Total interest = $5,000
- Solving the payment formula gives a rate of about 7.420% a year
Real-Life Examples
- Checking a dealer offer: $25,000 at $500 for 60 months is about 7.42%.
- A mortgage: $300,000 at $1,896.20 a month for 30 years is about 6.50%.
- Buy now, pay later: $1,200 repaid at $110 a month for 12 months is about 18.0% a year.
- A loan from a friend: $5,000 repaid at $450 a month for a year is about 14.5%.
Interest Rate vs APR
- Interest rate: the cost of borrowing the money itself.
- APR: the yearly cost including some fees, so it is often a bit higher.
- To compare offers: use APR. Try our APR Calculator.
Rate for a $10,000 Loan Over 5 Years
| Monthly payment | Total interest | Interest rate |
|---|---|---|
| $175.00 | $500.00 | 1.94% |
| $185.00 | $1,100.00 | 4.18% |
| $193.33 | $1,599.80 | 6.00% |
| $200.00 | $2,000.00 | 7.42% |
| $210.00 | $2,600.00 | 9.50% |
| $225.00 | $3,500.00 | 12.50% |
| $250.00 | $5,000.00 | 17.27% |
What Affects Your Rate
- Credit score: higher scores usually get lower rates.
- Term: longer loans often carry higher rates.
- Collateral: secured loans, like car loans, often cost less than unsecured ones.
- Market rates: rates follow the wider economy.
Common Mistakes to Avoid
- Including insurance or extras in the payment. Use only the loan payment.
- Mixing years and months. Check the term unit.
- Comparing only the payment. A longer term lowers the payment but can raise the rate and total interest.
- Ignoring fees. Fees raise the true cost, which APR shows.
- Using the price instead of the amount borrowed. Subtract your down payment.
Frequently Asked Questions
Enter the loan amount, monthly payment and term here. The calculator solves the payment formula for the rate.
Not a simple one. The rate is found by trial, which this calculator does instantly.
It depends on the loan type, your credit and the market. Compare offers from several lenders.
APR includes some fees as well as interest, so it shows the fuller cost.
The rate after monthly compounding: (1 + monthly rate)¹² − 1.
Yes. Use the principal and interest payment only, without taxes and insurance.
Interest is charged for more months, so total interest rises.
Then no positive rate fits, and the loan would never be repaid. Check your numbers.
If the payments add up exactly to the loan amount, the rate is 0%.
This is built for loans. For growth of savings, try our CAGR or APY calculators.
No. Add fees to the loan amount only if they are financed.
Enter each offer here to see its rate, then compare the total interest too. A lower payment over a longer term can still cost more in total. For offers with fees, compare the APR on each Loan Estimate.
Not directly. Leases have a money factor and a residual value, so a loan formula does not fit. Our Car Lease Calculator handles leases.
Very accurate for fixed-payment loans. Lenders may round differently by a few hundredths.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Consumer Financial Protection Bureau, Interest rate vs APR | How interest rates and APR differ. | https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-loan-interest-rate-and-the-apr-en-733/ |
| Wikipedia, Amortization calculator | The loan payment formula. | https://en.wikipedia.org/wiki/Amortization_calculator |