How Do You Calculate Compound Interest?

Calculate compound interest by multiplying the principal by a growth factor for every compounding period. In IB Mathematics: Applications and Interpretation, you may use the compound-interest formula or your GDC's finance application.

The Method

For an initial investment with no additional payments, use

$$A=P\left(1+\frac{r}{100k}\right)^{kn}$$

where:

• $A$ is the final amount;
• $P$ is the principal, or initial investment;
• $r$ is the annual percentage interest rate;
• $k$ is the number of compounding periods per year;
• $n$ is the number of years.

The interest earned is not the same as the final amount. It is

$$I=A-P.$$

Worked Example

Suppose \1000$is invested for$3$years at$4.8%$perannum,compoundedmonthly\mathrm{.}Sin$k=12$:

$$A=1000\left(1+\frac{4.8}{100(12)}\right)^{12(3)}.$$

Evaluating with a GDC gives

$$A=\$1154.55.$$

Therefore, the compound interest earned is

$$I=1154.55-1000=\$154.55.$$

The key is consistency between the periodic interest rate and the number of periods. Monthly compounding uses a monthly rate of $4.8\%/12=0.4\%$ and $12\times3=36$ periods. This means each month's balance becomes $1.004$ times the previous balance, so earlier interest also earns interest.

Using the finance solver, set $N=36$, $I\%=4.8$, $PV=-1000$, $PMT=0$, , and , then solve for . The result is positive because the initial investment was entered as money paid out.

For a GDC finance solver, enter the number of periods, interest rate, present value and payment frequency correctly. The present value and final value normally require opposite signs because one represents money paid out and the other money received.

A common misconception is to divide the rate by $12$ but forget to multiply the number of years by $12$. Both the periodic rate and the total number of periods must match the compounding frequency.

IB Exam Technique

This is SL 1.4 Financial applications, studied at both SL and HL. Show the formula substitution or finance-solver inputs, retain full GDC precision, and give money to two decimal places; deriving the compound-interest formula is not required.