Two loans can have the same amount, the same rate, and the same term, yet cost different amounts of total interest. The reason is the amortization system: the rule that splits each payment between interest and principal. The French and German systems are the two most common, and they behave very differently.
How it works
In the French system, the total payment stays the same every month. Early payments are mostly interest, and the principal share grows over time. In the German system, the principal share stays the same every month, so the total payment starts higher and falls as the balance shrinks. Because the German system repays principal faster early on, less interest builds up, and the total interest is lower for the same loan.
Step by step
- Write down the loan amount, the monthly interest rate, and the number of payments.
- For the French system, use the fixed-payment formula: payment = amount x rate x (1+rate)^n / ((1+rate)^n – 1).
- For the German system, divide the amount by the number of payments to get the fixed principal share.
- For each German payment, add interest on the remaining balance to the fixed principal share.
- Add up all payments in each system and subtract the loan amount to get total interest for each.
- Compare: the German system usually wins on total interest but demands higher payments at the start.
Worked example
Borrow $120,000 at 0.5 percent monthly for 120 months. French payment: about $1,322 per month, total paid about $158,600, total interest about $38,600. German system: principal share is $1,000 per month. First payment is $1,000 + $600 interest = $1,600. Last payment is $1,000 + $5 interest = $1,005. Total interest is about $36,300. The German system saves roughly $2,300 in interest here, but the first payments are about $278 higher per month.
Common mistakes
- Comparing only the monthly payment and ignoring total interest over the whole loan.
- Assuming the German system always has lower payments. It starts higher, not lower.
- Using the annual rate as the monthly rate without dividing by 12.
- Forgetting fees and insurance, which sit outside the amortization table but still cost money.
Try it with the free tool
You can follow every step above by hand, but the free tool below does the same calculation instantly. Try your own numbers in it, then check one result by hand so you trust the method as well as the answer. Open the full tool here: open the tool.
Checklist before you finish
- Write down every input number first, with its unit, before you calculate anything.
- Work through the steps in order, and do not skip the unit conversions.
- Check the answer against the worked example above: is it the right size, and does the direction make sense?
- Round only at the end, and keep the unrounded figure for any follow-up calculation.
Practice with your own numbers
Pick three cases of your own and work each one by hand. First, try a simple round-number case you can check mentally. Second, try a realistic case with awkward numbers, the kind you will actually meet. Third, try an edge case, such as a very small or very large input, and confirm the answer still behaves sensibly. If any case gives a surprising result, re-check the units and the formula step by step before you trust it.
If your answer looks wrong
Most errors come from a small set of causes. Check that you used the same units throughout, that you divided where the formula divides and multiplied where it multiplies, and that you applied any percentage as a decimal. Check the order of operations: powers and brackets come before multiplication and division, which come before addition and subtraction. Finally, test the method on the worked example in this guide. If your method reproduces the example answer, the method is right and the inputs deserve a second look.
Quick tips
Choose the French system if a steady payment matters most for your budget. Choose the German system if you can afford higher early payments and want to pay less interest overall. Always ask your lender for the full payment schedule before you sign.