Two seemingly opposite phenomena obey the same mathematics: a loan that costs more than you expect because interest piles up, and savings that grow faster than you imagine for the same reason. Understanding the mechanics through a few worked examples, which you can redo with a calculator, helps you compare offers without being impressed by them.
A loan's monthly payment
For a loan with constant payments, the payment M is calculated as: M = P × i ÷ (1 − (1 + i)⁻ⁿ), where P is the amount borrowed, i the rate per period (the annual rate divided by 12 for monthly payments) and n the number of payments. Each payment is the sum of two parts: the month's interest (remaining balance × i) and the repayment of principal. At the start, interest weighs heavily; it shrinks as the remaining balance falls.
Example: 200,000 borrowed at 4% over 25 years (300 payments). The monthly rate is 0.333%. In the first month, interest is 200,000 × 0.04 ÷ 12 ≈ 666.67, and the payment is about 1,055.67, of which only 389 repays principal. The total repaid is about 316,702, nearly 116,702 of interest.
The effect of term and rate
| Rate | Term | Monthly payment | Total interest |
|---|---|---|---|
| 4% | 20 years | ≈ 1,211.96 | ≈ 90,871 |
| 4% | 25 years | ≈ 1,055.67 | ≈ 116,702 |
| 5% | 25 years | ≈ 1,169.18 | ≈ 150,754 |
Stretching the term from 20 to 25 years lowers the payment by about 156 but costs nearly 26,000 more in interest. One extra point of rate over 25 years adds nearly 34,000. That is why comparing offers on the monthly payment alone is misleading: look at the total cost of credit.
Simulating with Loan & Mortgage Calculator
- Enter the amount, annual rate and term (in years or months). The payment, total interest and cost of credit show live. Currency is free.
- Open the amortization schedule: each instalment details interest, principal repaid and remaining balance, by year or instalment by instalment, with CSV export for Excel or LibreOffice.
- In the options, add insurance (as % per year of the initial principal), up-front fees, an extra payment with each instalment and a one-off early repayment: the tool shows the interest and time saved.
- Compare several scenarios by changing one value at a time.
The maths is done in whole cents, with no rounding drift, and the last instalment clears the principal exactly. The effective annual rate includes insurance and fees. The result remains indicative: the exact calendar, insurance on remaining balance, payment holidays or lender-specific fees can change the real amounts.
Compound interest
With compound interest, a period's interest is added to the principal and itself earns interest. The final balance is P × (1 + r)ⁿ for an annual rate r over n years. Example: 10,000 invested at 5% a year, no withdrawals.
| Term | Final balance | Of which interest |
|---|---|---|
| 10 years | ≈ 16,288.95 | ≈ 6,288.95 |
| 20 years | ≈ 26,532.98 | ≈ 16,532.98 |
| 30 years | ≈ 43,219.42 | ≈ 33,219.42 |
After 30 years, interest is more than three times the starting sum. This explains the advice to start early: time matters more than amount. A rough rule, the “rule of 72”, estimates doubling time: 72 ÷ 5 = 14.4 years (the exact calculation gives 14.2 years).
Common mistakes
- Comparing two loans on the monthly payment alone.
- Forgetting insurance and fees: the real cost is higher than the nominal rate.
- Counting on a guaranteed return for savings: an assumed rate is not a promise.
- Ignoring inflation and fees in a savings simulation.
- Confusing nominal and effective rate.
Honest limits
- These calculators give indicative simulations, not financial advice: for an important decision, see a licensed professional.
- Real returns vary, are not guaranteed, and fees and taxes are not included.
- Each lender's rules (360- or 365-day calculation, insurance, penalties) may differ.
Frequently asked questions
Why do you mostly pay interest at the start of a loan?
Because interest is calculated on the remaining balance, which is highest at the start. As the balance falls, the interest share shrinks.
Is early repayment always worthwhile?
It reduces future interest, but penalties may apply under your contract. The tool shows the interest and time saved.
What is the effective annual rate?
It is the rate that accounts for compound interest, insurance and fees: it reflects the real cost better than the nominal rate.
Are the results financial advice?
No. They are indicative mathematical simulations; consult a professional for an important decision.
Are my figures sent anywhere?
No. All calculations are done in your browser.