Amortization Calculator

📜 Historical Background

The term 'French amortization' derives from its widespread use in French banking during the 19th century, though the mathematics of level-payment loans dates to early compound interest calculations. The system became the global standard because it solved a practical problem: borrowers wanted predictable monthly payments for budgeting, while lenders wanted guaranteed returns. The formula creates equal payments by front-loading interest—a consequence of charging interest on the outstanding balance. In the United States, French amortization became ubiquitous after the Federal Housing Administration (FHA) standardized the 30-year fixed-rate mortgage in 1934. Before this, mortgages were typically short-term balloon loans requiring refinancing every 5-10 years, which proved disastrous during the Great Depression when banks failed and refinancing became impossible. The level-payment, fully-amortizing mortgage became the foundation of American homeownership.

🔬 Scientific Basis

French amortization derives from the ordinary annuity formula. Given principal P, monthly rate r, and n payments, the payment amount M satisfies the present value equation: P = M × [(1-(1+r)^(-n))/r]. Rearranging yields the standard formula. Each month, interest accrues on the remaining balance (Interest = Balance × r), and the remainder of the payment reduces principal (Principal = M - Interest). This creates the characteristic pattern: Month 1 of a $300,000, 30-year, 6% mortgage ($1,799 payment) shows $1,500 interest and only $299 principal. By Month 180 (halfway), it's $1,100 interest and $699 principal. By Month 360, it's $9 interest and $1,790 principal. The borrower pays $647,515 total—$347,515 in interest—but gets stable, predictable payments. The front-loaded interest structure reflects the mathematics of charging interest on declining balances; it's not a choice but a consequence of the formula.

💡 Practical Examples

• $400,000 mortgage at 7% for 30 years: Payment = $2,661. Month 1: $2,333 interest, $328 principal. After 5 years: paid $159,660, but only $22,000 went to principal. Balance: $378,000. After 15 years: balance $287,000.
• Impact of extra payments: Same loan, add $200/month extra to principal. Total interest drops from $558,000 to $418,000 (saves $140,000). Payoff accelerates from 30 years to 23 years.
• Amortization reset warning: $400,000 loan, 10 years in ($330,000 balance). Refinancing to new 30-year loan restarts the clock—next 10 years of payments will again be mostly interest, even if rate is lower.

⚖️ Comparison with Other Methods

French amortization produces the most predictable cash flow but the highest total interest cost compared to German (constant principal) or accelerated payment strategies. The difference is significant: on a $300,000, 30-year, 6% loan, French amortization costs $347,515 in interest; German amortization with same average payment would save approximately $30,000. However, German amortization starts with higher payments ($2,250 vs $1,799), which many borrowers can't afford. Biweekly payment strategies under French amortization (26 half-payments = 13 monthly payments annually) effectively add one extra payment per year, reducing a 30-year mortgage to approximately 24 years and saving substantial interest. The front-loading of interest is often misunderstood—it's not a bank trick but a mathematical consequence of compound interest on declining balances.

⚡ Pros & Cons