Formula
loan = payment × (1 − (1 + r)⁻ⁿ) ÷ r — solved for the monthly rate rannual rate = r × 12
- n — number of monthly payments
- There is no closed-form solution, so r is found numerically (bisection).
The tool tries monthly rates until the payments exactly repay the loan.
Worked example
10,00,000 repaid at 8,678.23 for 20 years
- Loan amount
- 1,000,000
- Monthly payment (EMI)
- 8,678.23
- Loan tenure
- 20
- Tenure in
- Years
Interest rate (per year)
8.5%
Effective annual rate (with monthly compounding): 8.8391%
Monthly rate: 0.70833%
Total interest over the loan: 1,082,775.2
How it works
A loan of 10,00,000 repaid with 8,678.23 a month for 20 years works out to an annual rate of 8.5%. It also reports the effective annual rate, which is higher (about 8.84%) because interest compounds monthly.
Use it to check a quoted rate against the EMI you are actually charged — if the rate implied by your payment is higher than the one advertised, fees or insurance may be bundled in. If the payments over the whole term don't even add up to the amount borrowed, the numbers can't be right and the tool says so. To go forward, from a rate to an EMI, use the EMI Calculator; for the schedule see the Amortization Schedule Calculator.
Assumptions and limits
- Equal monthly payments paid at the end of each month; no balloon payment or fees.