The formula
M = P × r(1+r)ⁿ ÷ ((1+r)ⁿ − 1)
What the variables mean
- P — loan principal (amount borrowed)
- r — monthly interest rate as a decimal (annual rate ÷ 12)
- n — total monthly payments (years × 12)
Worked example: $300,000 at 6.5% for 30 years
Plug the numbers in
- 1
Convert the rate
Monthly r = 6.5% ÷ 12 = 0.005417
- 2
Count the payments
n = 30 × 12 = 360
- 3
Compute (1+r)ⁿ
(1.005417)³⁶⁰ ≈ 7.0287
- 4
Apply the formula
M = 300,000 × (0.005417 × 7.0287) ÷ (7.0287 − 1) ≈ $1,896.20
Try it
Use our mortgage calculator for instant payments, total interest and an amortization preview.
Does this include taxes and insurance?
No — the closed-form formula returns principal + interest only. Lenders escrow property tax and insurance on top.
Why is early-mortgage interest so high?
Each payment is constant, but early in the loan principal is large — so interest (r × principal) dominates the split.
Related converters
The tools mentioned in this guide — one tap away.
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