How Loan Payments Are Calculated
A fixed-rate loan has the same payment every month. Each payment covers the interest that has built up plus a slice of the amount you borrowed. Here is the formula behind that number.
The formula
Monthly payment = P × i ÷ (1 − (1 + i)−n)
- P is the amount borrowed.
- i is the monthly interest rate: the yearly rate (APR) divided by 12.
- n is the number of monthly payments: years × 12.
Worked example
Borrow 250,000 at 6.5% APR for 30 years. The monthly rate is 0.065 ÷ 12 = 0.0054167 and n is 360. The payment works out to about 1,580.17 per month. Over 360 payments you pay 568,861.22 in total, which means 318,861.22 is interest.
A shorter term costs less overall
| Term | Monthly payment | Total paid | Total interest |
|---|---|---|---|
| 30 years | 1,580.17 | 568,861.22 | 318,861.22 |
| 15 years | 2,177.77 | 391,998.31 | 141,998.31 |
Halving the term raises the monthly payment by roughly 38% in this example, but cuts the interest by more than half.
Simple and compound interest
Loans use the formula above, where interest is charged on the remaining balance. Savings often grow with compound interest. For example, 1,000 at 5% for 3 years earns 150 with simple interest (1,150 total) but 157.63 with yearly compounding (1,157.63 total).
What the formula leaves out
Real loans can include fees, insurance, taxes and different rounding, and variable-rate loans change over time. Treat the result as an estimate, not an offer, and check the official figures with your lender.