1.12.2 Compound interest

Compound interest is computed on the principal as well as the interest collected over the previous period.

• It is different from simple interest where interest is only paid on the principal amount

• Simple interest increases by the same amount every time, but compound interest increases by an increasing amount every time.

• It is calculated by

\( A=P(1+\frac{r}{100})^t \)

Where

• \( A \) is the total amount

• \( P \) is the principal amount

• \( r \) is the interest rate per year

• \( t \) is the duration in years

Worked example:

Gretal invests \( $5000 \) at a rate of \( 2 \)% per year compound interest.

Calculate the value of her investment at the end of \( 3 \) years.

Substitute \( P=5000 \) , \( r=2 \) and \( t=3 \) in the formula \( A=P(1+\frac{r}{100})^t \)

\( A=5000(1+ \frac{2}{100})^3 \)

\( A=5306.04 \)

The value of investment at the end of \( 3 \) years is \( $5306.04 \)