Monthly Loan Payment
Fixed monthly payment for an amortizing loan.
Formula
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Example
Used for mortgages and car loans
How it works
This formula gives the constant payment needed each month to pay off a loan that charges compound interest and is fully repaid by the end of the term. It works by balancing two things: each payment must cover the interest added that month, and the rest must reduce the principal, so the payment amount is chosen so the remaining balance reaches zero after n payments. The formula comes from summing the discounted value of all equal future payments and solving for the payment size.
When to use it
Use this when a loan is repaid with equal monthly installments and the interest is compounded monthly, such as many student loans, personal loans, and equipment financing. It is appropriate when you know the amount borrowed, monthly interest rate, and total number of monthly payments.
Worked example, step by step
Suppose you borrow P = 12,000 at a monthly interest rate of r = 0.005 for n = 36 months. M = P[r(1+r)^n] / [(1+r)^n - 1] M = 12,000[0.005(1.005)^36] / [(1.005)^36 - 1] (1.005)^36 ≈ 1.19668 M = 12,000[0.005 × 1.19668] / [1.19668 - 1] M = 12,000[0.0059834] / 0.19668 M ≈ 71.8008 / 0.19668 M ≈ 365.10 Monthly payment ≈ $365.10
Common mistakes to avoid
- Using the annual interest rate instead of converting it to a monthly rate
- Forgetting that n is the total number of monthly payments, not years
- Treating the formula as simple interest instead of compound interest
Did You Know?
Early payments are mostly interest, later ones mostly principal.
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