Mortgage Monthly Payment (EMI)
Fixed monthly repayment on a mortgage.
Formula
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Example
P=$300k, r=0.005, n=360: M ≈ $1,798
How it works
This formula gives the fixed monthly payment needed to pay off a loan of principal P over n months at a constant monthly interest rate r. It works by setting the present value of all future equal payments equal to the amount borrowed, so each payment covers that month’s interest plus a portion of the remaining balance. Because interest is charged on the unpaid balance, the early payments are mostly interest and the later payments reduce principal more quickly.
When to use it
Use this when analyzing a standard fixed-rate mortgage or any amortizing loan with equal monthly payments. It is useful for comparing loan offers, estimating affordability, or checking whether a payment schedule will fully pay off the balance by the end of the term.
Worked example, step by step
Suppose a borrower takes a loan of P = $240,000 at a monthly interest rate of r = 0.0045 for n = 240 months. Step 1: Compute (1 + r)^n = (1.0045)^240 ≈ 2.9250 Step 2: Compute the numerator: P × r × (1 + r)^n = 240000 × 0.0045 × 2.9250 ≈ 3159.00 Step 3: Compute the denominator: (1 + r)^n - 1 = 2.9250 - 1 = 1.9250 Step 4: Divide: M = 3159.00 / 1.9250 ≈ 1640.52 Final answer: the monthly mortgage payment is about $1,640.52.
Common mistakes to avoid
- Using the annual interest rate directly instead of converting it to a monthly rate
- Forgetting that n must be the total number of monthly payments, not the number of years
- Treating the result as the total cost of the loan instead of just the monthly payment
Did You Know?
Early mortgage payments are almost all interest — principal only overtakes interest years into the loan.
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