Payment calculator

Two ways to think about a loan payment

Most people approach a loan from one of two directions. Either they know how much they need to borrow and want to know what the monthly bill will look like, or they know exactly what they can comfortably afford each month and want to know how long it'll take to pay the loan off at that rate. This calculator handles both directions using the same underlying loan amortization math, just solved for a different unknown each time.

Finding the monthly payment

When the loan amount, rate, and term are all known, the monthly payment comes from the standard fixed-payment loan formula. This is the same math used behind mortgage, auto loan, and personal loan payments — a fixed dollar amount that, if paid every month for the full term, exactly pays off the balance including all accrued interest.

• Payment = P × r / (1 − (1 + r)^−n), where P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments.

Finding the payoff time

When you flip the question around — "I can pay $400 a month, how long until this is paid off?" — the same formula gets rearranged to solve for the number of payments instead. There's an important catch here: your monthly payment has to be larger than the interest charged in the very first month, or the balance will never actually go down. If your budgeted payment is too low, the calculator will let you know rather than showing a misleading answer.

• Number of payments = −ln(1 − r×P/Payment) / ln(1 + r)

A worked example

Borrow $20,000 at 6% annual interest and pay $400 a month. Plugging into the formula above, it takes roughly 57.7 months — a little over 4 years and 9 months — to pay off the loan, with the total interest paid coming out to around $3,072 over that time.

Known values	What this calculator finds
Loan amount, rate, term	Fixed monthly payment
Loan amount, rate, monthly budget	Time to pay off (months/years)