Loans & Savings

Geometric series in your bank account

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Regular savings form a geometric series: total $= A\frac{(1 + r)^n - 1}{r}$.
• A loan of $L$ needs payments $\frac{rL}{1 - (1 + r)^{-n}}$.
• Early payments mostly cover interest; compounding works for and against you.

Steps

1. Compound interest
2. Ten years of saving
3. Pay off a mortgage
4. Interest-only
5. Three years at 5%
6. The rule of 72