How loan and mortgage payments are calculated
Almost every fixed-rate personal loan and mortgage uses the standard (French) amortisation system: the payment is the same every month, but the share that pays interest and the share that repays principal changes each month. Understanding it helps you compare offers and choose a term. The examples in this guide are calculated with the same formulas QuickToolio's calculators use.
The payment formula
Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount borrowed, r the monthly interest rate (annual rate divided by 12 and by 100) and n the number of monthly payments (years × 12). If the rate were 0, the payment would simply be the principal divided by the number of months.
Example: 15,000 at 7% over 5 years. r = 0.07 ÷ 12 ≈ 0.005833 and n = 60. The payment comes to 297.02 a month; in total you pay 17,821.08, of which 2,821.08 is interest.
Why early payments are mostly interest
Each month you pay interest on what you still owe, and the rest of the payment reduces the debt. On a 160,000 mortgage at 3% over 30 years (674.57 a month), the first month 400.00 is interest and only 274.57 repays principal. Because the debt falls slowly, after 10 years you still owe 121,631.69 (less than a quarter repaid), and halfway through, after 15 years, 97,680.91 remains.
That's why overpaying in the early years saves far more interest than doing it at the end: every unit repaid stops generating interest for the whole remaining term.
How much the term and rate change things
- Term: the same 15,000 at 7% over 3 years raises the payment to 463.16, but interest drops from 2,821.08 to 1,673.63.
- A 160,000 mortgage at 3%: over 30 years, 674.57 a month and 82,843.92 interest; over 20 years, 887.36 a month and 52,965.48 interest.
- Rate: that same 30-year mortgage at 4% instead of 3% raises the payment to 763.86 and total interest to 114,991.21, almost 32,000 more for one point.
A longer term makes the payment easier, but makes the total much more expensive. Comparing offers on the monthly payment alone is the easiest way to get it wrong.
Nominal rate, APR and what the payment leaves out
The formula uses the nominal interest rate. The APR adds fees and costs and is for comparing offers, not for calculating the payment. QuickToolio's calculators treat the rate you enter as nominal and don't include arrangement fees, linked insurance, valuation, legal costs or taxes.
- On a mortgage, the deposit directly reduces the amount financed: with a 200,000 home and a 40,000 deposit, 160,000 is borrowed.
- On a variable-rate mortgage, the payment is recalculated at each review: the formula applies to the current period, not the whole term.
- The real monthly outgoing often adds home or life insurance, which isn't part of the loan.
The other side: compound interest on savings
The same mechanism that makes a long loan expensive makes savings grow: each period's interest is added to the balance and earns interest in turn. 10,000 at 5% for 10 years becomes 16,470.09 with monthly compounding and 16,288.95 with annual compounding, before inflation, fees and taxes.
Frequently asked questions
Is the payment always the same?
Yes, as long as the interest rate doesn't change. What changes each month is the split: at first it's mostly interest, at the end mostly principal.
When overpaying, is it better to shorten the term or lower the payment?
Shortening the term generally saves more, because it keeps the payment and removes whole months of interest. Lowering the payment eases the monthly budget but saves less interest overall.
Can I use the APR in the calculator?
It isn't correct: the payment is calculated with the nominal rate. The APR includes costs and is meant for comparing offers, so using it gives a slightly higher payment than the real one.
Why does my bank quote a payment a few cents different?
Because of rounding, payment dates that don't fall on exact months, or how the first period's interest is calculated. Larger differences usually come from included insurance or fees.