Equal Principal vs Equal Payment Calculator (German vs French Amortization)
Compare the two classic amortization methods: equal (level) payments — the French system — versus equal principal payments — the German system — with first and last payments, total interest and a yearly schedule.
How it works
Equal payment (French): A = P × i ÷ (1 − (1 + i)⁻ⁿ), interest = A × n − P · Equal principal (German): principal each month = P ÷ n, payment k = P ÷ n + (P − (k − 1) × P ÷ n) × i, total interest = P × i × (n + 1) ÷ 2
With equal payments (the French system, used by most mortgages and car loans) every installment is the same and the interest share shrinks over time. With equal principal (the German system, common in some European and Latin American banks) you repay the same slice of principal each month plus interest on the remaining balance, so payments start higher and fall steadily. Because the balance drops faster, the German system always costs less interest at the same rate — the trade-off is a heavier start.
Worked example
A 100,000 loan at 12% over 5 years: with equal payments the installment is 2,224.44 every month and total interest 33,466.69. With equal principal you repay 1,666.67 of principal each month plus interest, so the first payment is 2,666.67 and the last 1,683.33, for total interest of 100,000 × 1% × 61 ÷ 2 = 30,500. Equal principal saves 2,966.69 of interest; its payment drops below the equal payment from month 28.
Sources: Wikipedia — Amortizing loan · Wikipedia — Amortization calculator
Frequently asked questions
Which amortization system is cheaper?
Equal principal (German) always pays less total interest at the same rate and term, because the debt falls faster. Equal payment (French) is easier to budget because the installment never changes.
Why is the first German payment so high?
It includes a full slice of principal plus interest on the whole loan. Lenders check affordability against that first payment, so you may qualify for a smaller loan.
Is there an American system too?
The “American” system pays only interest each period and the whole principal at the end — that is an interest-only or bullet loan.
Can I get German-style savings with a French loan?
Yes, by making extra principal payments: each one shortens the term and cuts interest the same way.
Related calculators
Estimates for education and planning, not financial advice. Lenders’ contracts, fees, day-count and rounding rules differ — check the official cost disclosure (APR / TAE / CAT) in your loan or card agreement before deciding.