Quick answer: the monthly payment on a fixed-rate loan is M = P × r ÷ (1 − (1 + r)−n), where P is the amount borrowed, r is the monthly interest rate (annual rate ÷ 12) and n is the number of monthly payments. The same formula is used for the "monthly installment", "loan repayment" and "EMI".
The formula and what each letter means
| Symbol | Meaning | Also called |
|---|---|---|
| M | Monthly payment | installment, repayment, EMI, PMT |
| P | Amount borrowed | principal, loan amount, PV |
| r | Monthly interest rate | annual rate ÷ 12, as a decimal |
| n | Number of payments | years × 12 |
If the interest rate is 0%, the formula is simply M = P ÷ n.
Step-by-step example
Borrow $12,000 at 9% APR for 4 years.
- Monthly rate: 9% ÷ 12 = 0.75%, or 0.0075.
- Number of payments: 4 × 12 = 48.
- Growth factor: (1.0075)−48 ≈ 0.6986.
- Denominator: 1 − 0.6986 = 0.3014.
- Numerator: 12,000 × 0.0075 = 90.
- Payment: 90 ÷ 0.3014 ≈ $298.62 a month.
Over 48 months you will pay about $14,334 in total, so roughly $2,334 is interest.
Monthly interest payment formula
Each month's interest is the current balance times the monthly rate:
In month one, the balance is $12,000, so interest is 12,000 × 0.09 ÷ 12 = $90.00. The remaining $208.62 of the payment reduces the balance to $11,791.38. In month two, interest is charged on the smaller balance: $88.44. On an interest-only loan, you pay just this interest amount each month and the balance does not fall.
Regular payment versus flat-rate quotes
The formula above assumes a "reducing balance" loan, where interest is charged only on what you still owe. Some lenders quote a flat rate instead, charging interest on the full original amount for the whole term. The payment is (P + P × rate × years) ÷ months. At a 9% flat rate, the same $12,000 loan costs (12,000 + 4,320) ÷ 48 = $340.00 a month, noticeably more than $298.62. When you compare offers, ask for the APR on a reducing-balance basis.
The spreadsheet shortcut
In Excel or Google Sheets, PMT takes the monthly rate, the number of payments and the loan amount (as a negative number) and returns $298.62.
Common mistakes
- Using the annual rate as r instead of dividing by 12.
- Mixing years and months, for example using n = 4 instead of 48.
- Forgetting fees, insurance and taxes that may be added on top.
To skip the arithmetic, use the loan calculator, or open the amortization calculator to see every payment split into interest and principal.