# Interest Rate Calculator

> Work out the interest rate on a loan from the amount borrowed, the monthly payment and the number of payments, as an annual rate and an effective rate.

Category: Finance · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/interest-rate-calculator

If you know what you borrow, what you repay each month and for how long, the interest rate is fixed by the maths. This calculator finds it, so you can check an offer or compare loans.

Also called: Loan rate calculator.

## Inputs
- Amount borrowed (default 25000)
- Monthly payment (default 483.32)
- Number of monthly payments (unit months; default 60)
- Currency

## Results
- Annual interest rate
- Effective annual rate
- Monthly rate
- Total interest
- Total of all payments

## Formula

```
Find i such that Payment = L × i(1+i)^n ÷ ((1+i)^n − 1) (solved numerically by bisection);  Annual rate = 12 × i;  Effective rate = (1 + i)^12 − 1
```

Where:
- L: amount borrowed
- n: number of monthly payments
- i: monthly interest rate

## Worked example
1. Total repaid = 483.32 × 60 = $28,999.20, so interest = $3,999.20.
2. At i = 0.5% a month, 25,000 × 0.005 × 1.005^60 ÷ (1.005^60 − 1) = 483.32, matching the payment.
3. Annual rate = 12 × 0.5% = 6%; effective rate = 1.005^12 − 1 = 6.1678%.

**Result:** Borrowing $25,000 and repaying $483.32 a month for 60 months means a 6% annual interest rate.

## What the result means

If a lender quotes a lower rate than this calculator finds for the same payment, fees or add-ons have been folded into the payment. The effective rate is useful when comparing with savings rates.

## Assumptions and limits
- Payments are equal, monthly and start one month after the loan is made.
- The amount borrowed is what you actually receive; fees deducted upfront raise the true rate.
- This is the rate implied by the payments, not a regulatory APR, which may include specific fees under local rules.

## Questions

### Why is there no simple formula for the rate?

The payment formula cannot be rearranged for the rate, so it is found by trying rates until the payment matches, as financial calculators do.

### What if the payments add up to exactly what I borrowed?

Then the rate is 0%. If they add up to less, no positive rate fits.

## Related calculators
- [Loan Calculator](https://calculators.geekmidst.com/calculators/loan-calculator)
- [Finance Calculator](https://calculators.geekmidst.com/calculators/finance-calculator)
- [Auto Loan Calculator](https://calculators.geekmidst.com/calculators/auto-loan-calculator)
- [EMI Calculator](https://calculators.geekmidst.com/calculators/emi-calculator)

_This calculator gives estimates for planning. It is not financial advice, and lenders’ actual terms, fees and rounding may differ._

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/interest-rate-calculator