Amortized loans – declining balance, annuity, and the flat-rate trap
MathematicsSequences & Financial MathAges 17–18
Use it with your class: students open it from a link or a QR code, with no account needed.
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Enter the loan amount, annual interest rate, and term in months, then choose a repayment method: equal principal with interest on the declining balance, equal monthly payments (annuity), or flat interest calculated on the original principal. The chart splits each month's payment into principal and interest, plots the declining balance, and shows total interest — revealing that the real interest rate behind a "flat 1%/month" offer is nearly double the advertised figure.
Lesson: Financial mathematics
What it shows
A loan is repaid in monthly instalments that combine principal and interest. With equal principal, the same amount of principal is repaid every month and interest is charged on the declining balance, so payments fall over time. An annuity keeps the payment constant, A = P·i/(1 − (1 + i)⁻ⁿ) with monthly rate i, so the interest share shrinks while the principal share grows. Flat interest is charged every month on the original loan, which makes its effective rate far higher than the advertised rate. The simulation plots all three month by month.
How to use
Keep the default Loan amount, Interest rate and Term, and look at Equal monthly payments (annuity) first: compare the interest and principal parts of the first and last bars. Then switch the Repayment method to the other two options and compare total interest and the effective rate in the table. Finally double the Term and observe how the monthly payment and the total interest change.
Parameters you can change
- Loan amount 1–80
- Interest rate 1–36 %/year
- Term 3–240 months
- Repayment method Equal principal, interest on declining balance, Equal monthly payments (annuity), Flat interest on original principal
- Currency From the language, US dollar, Euro, Indian rupee, Indonesian rupiah, Saudi riyal
Questions to explore
- Why is flat interest more expensive than interest on the declining balance at the same advertised rate?
- If the term is doubled, how do the monthly payment and the total interest of an annuity loan change?
- In an annuity loan, why is the interest part of the payment largest in the first month?
