Financial Mathematics — Compound Interest, Annuities, and Loans

Money and time

Financial mathematics applies geometric growth to money. Because interest earns interest, invested money grows as a geometric sequence, and the IB expects fluency both with formulas and with a GDC's finance solver (the TVM, or "time value of money," solver).

Compound interest

If a principal $PV$ is invested at an annual interest rate $r\%$, compounded $k$ times per year for $n$ years, its future value is

$$FV = PV\left(1 + \frac{r}{100k}\right)^{kn}.$$

Worked example. You invest £5000 at $4\%$ per year compounded quarterly ($k=4$) for 6 years: $$FV = 5000\left(1 + \frac{4}{100 \times 4}\right)^{4 \times 6} = 5000(1.01)^{24} \approx 5000 \times 1.2697 \approx £6348.67.$$ The interest earned is about £1348.67. Compounding more frequently increases the return: the same money co