Loan Payment Calculator

How loan payments work

When you take out a loan and repay it in equal monthly instalments, you are using a process called amortization. Each payment is the same size, but the split changes over time: early on most of it covers interest, and later most of it pays down the balance. This calculator works out that fixed monthly payment for you.

where:

• M is the monthly payment
• P is the principal, the amount you borrow
• r is the monthly interest rate (the annual rate divided by 12)
• n is the total number of payments (years multiplied by 12)

How to use this calculator

1. Enter the loan amount, which is the amount borrowed.
2. Enter the monthly interest rate, as a decimal, not a percent.
3. Enter the total number of monthly payments.
4. Compute the monthly payment, then compare it with your budget.

The formula explained

The formula computes the fixed monthly payment, also called the installment amount, for an amortizing loan. It shows how the payment depends on the principal, the interest rate, and the number of months.

• M = monthly payment
• P = principal, or original loan amount
• r = monthly interest rate as a decimal
• n = number of monthly payments

Step by step method

1. Find the monthly interest rate by dividing the annual rate by \(12\) if needed.
2. Substitute \(P\), \(r\), and \(n\) into \(M = P \frac{r(1+r)^n}{(1+r)^n - 1}\).
3. Evaluate the exponent first, then the numerator and denominator, and divide to get \(M\).

Worked example

Problem. You borrow \(15000\) dollars at a monthly interest rate of \(0.005\) for \(60\) months. What is the monthly payment?

1. Substitute into the formula: \(M = 15000 \frac{0.005(1.005)^{60}}{(1.005)^{60} - 1}\).
2. Compute \((1.005)^{60} \\approx 1.34885\), so \(M \\approx 15000 \frac{0.005(1.34885)}{1.34885 - 1}\).
3. This gives \(M \\approx 289.99\).

Tips and common mistakes

• Make sure the rate you enter is monthly, because the formula uses a monthly interest rate.
• If the interest rate is \(0\), the formula does not work, so the payment is just \(P \\div n\).

Frequently asked questions