50-Year Mortgage Calculator
Compare 50-year vs 30-year mortgages with detailed financial analysis
Loan Details
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📊 Formulas & Definitions
Monthly Payment Formula
M = P × [r(1 + r)^n] / [(1 + r)^n – 1]
Where:
• M = Monthly payment
• P = Principal loan amount
• r = Monthly interest rate (annual rate / 12)
• n = Number of months (years × 12)
• M = Monthly payment
• P = Principal loan amount
• r = Monthly interest rate (annual rate / 12)
• n = Number of months (years × 12)
DTI (Debt-to-Income) Ratio
Required Income = (Monthly Payment × 12) / 0.28
The 28% rule is a standard lending guideline stating that your mortgage payment (including taxes,
insurance, HOA, and PMI) should not exceed 28% of your gross monthly income. This helps determine
the minimum income needed to qualify for the mortgage.
PMI (Private Mortgage Insurance)
Monthly PMI = (Loan Amount × PMI Rate / 100) / 12
PMI is required when the down payment is less than 20% of the home’s purchase price. It protects the
lender against default and typically costs 0.5-1% of the loan amount annually.
Equity Calculation
Equity = Home Value – Remaining Loan Balance
Equity represents your ownership stake in the home. It increases as you pay down the principal
and/or as the home appreciates in value. The remaining balance is calculated using an amortization
schedule.
Total Interest Paid
Total Interest = (Monthly Payment × Number of Payments) – Principal
This represents the total cost of borrowing over the life of the loan. The longer the loan term, the
more interest you’ll pay overall, even with lower monthly payments.
Break-Even Analysis
Break-Even Years = Extra Interest / Annual Payment Savings
This calculates how many years of lower monthly payments it would take to offset the additional
interest paid on a 50-year mortgage compared to a 30-year mortgage. This helps evaluate the true
cost of the extended loan term.
Amortization Formula
Remaining Balance = P × [(1 + r)^n – (1 + r)^p] / [(1 + r)^n – 1]
Where:
• P = Original principal
• r = Monthly interest rate
• n = Total number of payments
• p = Number of payments made
This formula calculates the remaining loan balance at any point during the loan term.
• P = Original principal
• r = Monthly interest rate
• n = Total number of payments
• p = Number of payments made
This formula calculates the remaining loan balance at any point during the loan term.
Key Terms Glossary
Principal: The amount borrowed, calculated as home price minus down
payment.
Interest Rate: The annual percentage charged by the lender for borrowing money.
Amortization: The process of paying off debt through regular payments over time.
PITI: Principal, Interest, Taxes, and Insurance – the components of a monthly mortgage payment.
LTV (Loan-to-Value): The ratio of the loan amount to the home’s value. Lower LTV means more equity.
Points: Prepaid interest that can lower your interest rate. One point equals 1% of the loan amount.
Interest Rate: The annual percentage charged by the lender for borrowing money.
Amortization: The process of paying off debt through regular payments over time.
PITI: Principal, Interest, Taxes, and Insurance – the components of a monthly mortgage payment.
LTV (Loan-to-Value): The ratio of the loan amount to the home’s value. Lower LTV means more equity.
Points: Prepaid interest that can lower your interest rate. One point equals 1% of the loan amount.
