Mortgage & Loan FAQ: How to Calculate Payments and Interest
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Worked US examples of the formulas lenders use: the fixed-rate monthly payment, how each month's interest is charged, total interest over the loan, simple interest, APR, affordability and home equity. Rates are annual percentages; amounts are in US dollars.
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How do I calculate a monthly mortgage payment?
For a fixed-rate loan, principal and interest M = P × r(1 + r)^n ÷ [(1 + r)^n − 1], where P is the loan amount, r is the annual rate ÷ 12 (as a decimal) and n is the number of monthly payments. Example: $320,000 at 6.5% for 30 years → r = 0.0054167, n = 360, M ≈ $2,022.62.
What else is included in my monthly mortgage payment?
Your total monthly payment is often principal + interest + property taxes + homeowners insurance (collected in escrow) + mortgage insurance and any HOA dues. The CFPB calls this PITI plus mortgage insurance. Use the escrow figures on your Loan Estimate rather than a guess.
How do I calculate the interest on a mortgage for one month?
Monthly interest = current loan balance × annual rate ÷ 12. On a $320,000 balance at 6.5%, the first month's interest is $320,000 × 0.065 ÷ 12 ≈ $1,733.33; the rest of the $2,022.62 payment (≈ $289.29) reduces principal. Each month interest is recalculated on the new, lower balance.
How do I calculate total interest over the life of a loan?
Total interest = (monthly principal-and-interest payment × number of payments) − loan amount. For the example above: $2,022.62 × 360 − $320,000 ≈ $408,143 in interest if you never prepay.
How does mortgage amortization work?
Each month: interest = balance × r; principal paid = M − interest; new balance = balance − principal paid. Because the balance falls, interest shrinks and principal grows every month while M stays fixed. On $320,000 at 6.5% for 30 years, month 1 splits $1,733.33 interest / $289.29 principal; by month 360 almost the whole payment is principal.
How do I calculate my remaining loan balance after k payments?
Balance after k payments B = P(1 + r)^k − M × [(1 + r)^k − 1] ÷ r. For $320,000 at 6.5% with M = $2,022.62, after 60 payments (5 years) B ≈ $299,555 — only about $20,445 of principal has been repaid, which is why early payments are mostly interest.
How do I calculate simple interest?
Simple interest I = P × r × t, where P is principal, r is the annual rate as a decimal and t is time in years. $10,000 at 5% for 3 years earns or costs $1,500. Mortgages are amortized instead: interest is charged monthly on the remaining balance.
What is the difference between interest rate and APR?
The interest rate sets your monthly payment. The APR spreads certain loan costs, such as points and lender fees, over the loan term and expresses the total yearly cost as a rate, so it is usually higher. Compare APRs across Loan Estimates for the same loan type.
How much house can I afford based on the monthly payment?
Reverse the payment formula: loan amount P = M × [(1 + r)^n − 1] ÷ [r(1 + r)^n]. Many lenders also check a debt-to-income ratio (total monthly debts ÷ gross monthly income); the CFPB notes 43% is a common qualified-mortgage reference point, though lenders set their own limits.
How do I calculate my home equity?
Home equity = current market value − all balances secured by the home (mortgage, HELOC, liens). Loan-to-value = loan balance ÷ home value. On a $400,000 home with a $250,000 balance, equity is $150,000 and LTV is 62.5%.
Related
Sources
- CFPB — What is included in a monthly mortgage payment? — principal, interest, taxes, insurance and escrow
- CFPB — What is the difference between a mortgage interest rate and an APR? — rate vs APR
- CFPB — What is a debt-to-income ratio? — DTI calculation and the 43% reference
- Federal Reserve — Consumer's Guide to Mortgage Refinancings / amortization basics — how amortized payments split interest and principal