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How loan payments are calculated: formula, example and what to watch for

· 2 min read

A loan's monthly payment depends on the amount, the monthly interest and the term. The formula looks complicated at first, but the idea is simple: you pay the same amount every month and part of it goes to interest, the rest to the principal.

The equal-payment (annuity) formula

Most personal loans have a fixed payment each month. It is found with this formula:

payment = amount × r / (1 − (1 + r)^(−n))

amount: the loan amount
r     : monthly interest rate (e.g. 3.5% → 0.035)
n     : term (number of months)

Example

For a 100,000 loan at 3.5% monthly interest over 24 months the math comes out like this:

payment        = 6,227.28
total repaid   = 6,227.28 × 24 = 149,454.79
total interest = 149,454.79 − 100,000 = 49,454.79

Because of rounding these figures can differ by a few cents from a lender's calculation.

Notice that interest weighs most in the early months

In the first month interest is charged on the whole balance: 100,000 × 0.035 = 3,500. Since the payment is 6,227.28, only 2,727.28 goes to the principal in month one. As the balance shrinks, interest gets smaller and the principal share grows. The repayment schedule shows this month by month.

A monthly rate is not the same as an annual rate

Multiplying 3.5% monthly by 12 and calling it "42% a year" is wrong, because interest compounds. The real annual cost is (1.035^12 − 1), about 51.1%. When comparing offers, look at the same kind of rate (all monthly or all annual compound).

Why does a lender's offer differ?

The formula only covers interest. Real loans may also add arrangement fees, insurance and, for some loan types, taxes charged on the interest. So a lender's payment can be higher than the one calculated here. The calculation gives a rough idea, and what counts is the lender's written offer.

Try it yourself

Enter the amount, monthly rate and term into the loan calculator to see the monthly payment, total repayment, total interest and the month-by-month schedule. Your numbers never leave your browser.

This article is general information, not financial advice. Read the lender's contract and total cost details before taking a loan.

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