Mortgage Calculator Calculators

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A mortgage is a home loan where the property serves as collateral. Monthly mortgage payments cover principal and interest (and often taxes and insurance — PITI). The payment is calculated using: M = P × [r(1+r)^n] / [(1+r)^n − 1], where P = loan principal, r = monthly interest rate, and n = total monthly payments. Understanding mortgage calculations helps buyers compare loan offers, determine affordability, plan for total interest costs, and evaluate the benefit of extra principal payments or refinancing.

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Monthly Mortgage Payment Formula

M = P × [r(1+r)^n] / [(1+r)^n − 1]

P = principal (loan amount); r = monthly rate = annual rate / 12; n = total payments = years × 12.

Example: $300,000 loan at 6.5% APR for 30 years: r = 0.065/12 = 0.005417; n = 360; M = 300,000 × [0.005417 × 1.005417^360] / [1.005417^360 − 1] = $1,896.20/month.

Total Cost Analysis

Total paid = M × n = 1,896.20 × 360 = $682,632. Total interest = 682,632 − 300,000 = $382,632 in interest over 30 years. This demonstrates why mortgage term matters: same loan at 6.5% for 15 years: M = $2,613.32/month; total interest = $170,398 — saving $212,234 by choosing the shorter term.

Amortization

Month 1: interest portion = $300,000 × 0.005417 = $1,625.00; principal portion = $1,896.20 − $1,625.00 = $271.20. Month 360: interest ≈ $10.20; principal ≈ $1,886.00. Early payments are mostly interest; later payments are mostly principal.

PMI and Down Payment

PMI (private mortgage insurance) required when down payment < 20%. PMI costs 0.5–1.5% per year on the loan balance. 20% down on $400,000 home = $80,000 down, $320,000 loan (no PMI). 5% down = $20,000 down, $380,000 loan + PMI ~$190–570/month.

Glossary

Monthly Mortgage Payment
M = P × [r(1+r)^n] / [(1+r)^n − 1]; P = principal; r = monthly rate; n = total payments; covers principal and interest; amortized so each payment is equal.
Amortization
The gradual paydown of a mortgage; early payments are mostly interest; later payments are mostly principal; same total monthly payment throughout (fixed-rate mortgage).
PMI (Private Mortgage Insurance)
Required when down payment is less than 20%; costs 0.5–1.5% of loan per year; protects the lender; eliminated when loan-to-value ratio reaches 80%.

Frequently Asked Questions

M = P × [r(1+r)^n] / [(1+r)^n − 1]. P = loan principal (home price minus down payment); r = monthly interest rate = annual rate/12; n = total number of monthly payments (years × 12). Example: $250,000 loan at 7% for 30 years: r = 0.07/12 = 0.005833; n = 360; M = 250,000 × [0.005833 × 1.005833^360] / [1.005833^360 − 1] = $1,663.26/month. In Excel: =PMT(0.07/12, 360, 250000) = −$1,663.26 (negative = payment outflow).

Example: $350,000 loan at 6.75% APR. 30-year mortgage: monthly = ~$2,270; total paid = $817,200; total interest = $467,200. 15-year mortgage: monthly = ~$3,096; total paid = $557,280; total interest = $207,280. Savings with 15-year: $259,920 in interest. The trade-off: monthly payment is $826 higher for the 15-year, but you save a quarter million in interest and build equity faster. If you can afford the higher payment, the 15-year mortgage is almost always financially better. Many buyers choose 30-year for lower monthly commitment but make extra principal payments equivalent to the 15-year payment when possible.

Amortization is the process of gradually paying down the mortgage through regular payments that each cover interest and principal. In early payments, most of the payment goes to interest because the balance is high (interest = balance × monthly rate). As principal decreases, the interest portion shrinks and the principal portion grows — same total payment, shifting composition. Month 1 on a $300,000 loan at 6%: interest = $300,000 × 0.005 = $1,500; principal = $1,799 − $1,500 = $299. After 20 years (240 payments): remaining balance ~$186,000; interest portion = ~$930; principal portion = ~$869. Full amortization schedule in Excel: use PPMT(rate, period, nper, pv) and IPMT(rate, period, nper, pv) functions for each payment.

Extra principal payments reduce the loan balance immediately, decreasing all future interest charges. Rule of thumb: extra payments early in the loan save the most — each extra dollar in year 1 eliminates 30 years of future interest on that dollar. Example: $300,000 at 7%, 30 years. Regular payment: $1,996/month; total interest = $418,527. Pay $200 extra/month from day one: payoff in ~24 years; total interest ≈ $330,000 — saving ~$88,000 and 6 years. Considerations: (1) Is your mortgage rate higher than safe investment returns? If mortgage = 7%, risk-free returns = 5%, pay down mortgage. (2) Do you have high-interest debt? Pay that first. (3) Is your emergency fund adequate? Build that before extra mortgage payments.