Loan Calculator

How a loan payment works

With a fixed-rate loan you pay the same amount every month. Each payment has two parts: theinterest on the balance you still owe, and the rest, which pays back part of theprincipal (the money you borrowed). This is called an amortizing loan, and it's how most personal loans, auto loans, and mortgages work.

At the start the balance is high, so most of each payment is interest. Over time the balance goes down, the interest part gets smaller and more of each payment goes to the principal. In the last payment, the balance reaches zero.

This calculator assumes monthly payments, a rate that doesn't change and no extra payments. It doesn't include insurance, taxes, or fees.

The formula

The fixed monthly payment is:

M = P × r / (1 − (1 + r)⁻ⁿ)

• M: monthly payment
• P: loan amount
• r: monthly interest rate, which is the annual rate divided by 12 (6% a year = 0.005)
• n: number of monthly payments (30 years = 360)

If the rate is 0%, the payment is simply the amount divided by the number of payments.

Worked example

You borrow 1,000 at 12% a year and pay it back in 3 months.

1. Monthly rate: 12% ÷ 12 = 1% = 0.01.
2. Payment: 1,000 × 0.01 / (1 − 1.01⁻³) = 10 / 0.029410 = 340.02.
3. Month 1: interest 1,000.00 × 0.01 = 10.00; principal 340.02 − 10.00 = 330.02; balance 669.98.
4. Month 2: interest 669.98 × 0.01 = 6.70; principal 333.32; balance 336.66.
5. Month 3: interest 336.66 × 0.01 = 3.37; principal 336.66; balance 0.00.

In total you pay 1,020.07: the 1,000 you borrowed plus 20.07 in interest. Notice how the interest goes down each month while the principal part goes up.