The Loan Payment Formula, Explained Simply

The formula

The monthly payment on a fixed-rate, fully amortized loan is: M = P × r × (1 + r)^n / ((1 + r)^n − 1).

P is the loan principal, r is the monthly interest rate (the annual rate divided by 12), and n is the total number of payments.

Why the formula works

Each payment covers the interest that has accrued since the last payment, plus some principal. Because interest is charged on the remaining balance, the interest portion shrinks every month and the principal portion grows — yet the total payment stays the same.

The (1 + r)^n term is what accumulates interest over the full term; dividing by (1 + r)^n − 1 spreads that total into equal installments.

A worked example

Take a $10,000 personal loan at 5% APR for 5 years. The monthly rate is 0.05 ÷ 12 = 0.004167, and there are 60 payments.

Plugging into the formula gives $188.71 per month. Over 60 payments that is $11,322.74 total, so you pay $1,322.74 in interest.

How the numbers change with your choices

Interest rate matters more than you might expect — the same loan at 8% instead of 5% jumps the payment to about $202.76 and total interest to about $2,166.

Term matters too: a 3-year version of the $10,000 loan at 5% costs $299.71 a month but only $789.52 in interest. Shorter terms cost more monthly but much less overall.

Frequently asked questions