How Loan Payments Are Calculated (With a Worked Example)

Most loans, from cars to mortgages, use the same method: a fixed monthly payment that stays the same while the balance shrinks. Early on, most of each payment is interest. Later, most of it pays down the loan itself.

The formula

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

M = monthly payment
P = amount borrowed
r = monthly interest rate (annual rate / 12)
n = number of monthly payments

A worked example

Borrow 10,000 at 6 percent a year for 3 years. The monthly rate is 0.06 / 12 = 0.005, and there are 36 payments. The formula gives a payment of about 304.22 a month. Over 36 months you pay about 10,951.90 in total, so the interest cost is about 951.90.

How the split changes

In the first month, interest is 0.005 x 10,000 = 50.00, so only about 254.22 of the 304.22 reduces the balance. Next month the balance is a little lower, so the interest is a little lower, and slightly more goes to principal. This pattern is called amortization.

What changes the cost most

• Interest rate: a lower rate cuts the total paid directly.
• Term: a longer loan lowers the monthly payment but raises the total interest, sometimes by a lot.
• Extra payments: money paid early goes straight to principal, which reduces future interest and shortens the loan.

Look out for

• The difference between the interest rate and the APR, which also includes fees.
• Early repayment charges, which some lenders add.
• Rates that change over time on variable loans.

Plug your own numbers into the Loan Calculator to see the monthly payment and the full schedule. To see how savings grow instead, try the Compound Interest Calculator, and use the Percentage Calculator for quick comparisons between rates.