How loan and mortgage interest works (and how to pay less)

Most personal loans, car loans and mortgages are amortizing loans: you pay the same amount every month, and each payment covers that month's interest plus a slice of the principal.

The monthly payment

For a fixed-rate loan the payment is:

M = P × r ÷ (1 − (1 + r)^−n)

where P is the amount borrowed, r the monthly rate (annual rate ÷ 12) and n the number of monthly payments.

Example: 15,000 at 6.5% over 5 years → 293.49 per month, and 2,609.53 of interest in total. Check it with the Loan calculator.

Why early payments are mostly interest

Interest is charged on the remaining balance. At the start the balance is highest, so most of the payment goes to interest; as the balance falls, more of each payment reduces the principal. The amortization table in the calculators shows this year by year.

Term length: lower payment, higher total cost

Stretching a loan lowers the monthly payment but increases the total interest, sometimes dramatically. On a 240,000 mortgage at 3.8%:

Term	Monthly payment	Total interest
20 years	≈ 1,429	≈ 103,000
25 years	≈ 1,240	≈ 132,000

Try your own numbers in the Mortgage calculator.

Extra repayments

Every extra amount you repay goes straight to the principal, so it stops generating interest for the rest of the loan. On that 25-year example, paying an extra 200 a month clears the loan in about 19 years 10 months and saves around 30,000 of interest. Check first whether your lender charges early-repayment fees.

APR vs interest rate

The interest rate only covers interest. The APR (annual percentage rate — TAEG in France) also includes mandatory fees and insurance, so it's the better figure for comparing offers.

The other side: saving

When you save, the same mathematics works for you — see Compound interest.

These calculators give estimates for planning. Your lender's figures are the ones that count; this isn't financial advice.