Compound Interest/Examples/Arbitrary Example 1

Example of Compound Interest

Let $\pounds 1000$ be invested for $2$ years at $8 \%$ per annum.

At the end of the $1$st $6$ months, the compound interest will be:

$I_1 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1000 = \pounds 40$

At the end of the $2$nd $6$ months, the compound interest will be:

$I_2 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1040 = \pounds 41 \cdotp 60$

At the end of the $3$rd $6$ months, the compound interest will be:

$I_3 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1081 \cdotp 60 = \pounds 43 \cdotp 26$

At the end of the $4$th $6$ months, the compound interest will be:

$I_4 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1124 \cdotp 86 = \pounds 44 \cdotp 99$

Hence the total interest earned will be $\pounds 169 \cdotp 85$.

$I = P \paren {\paren {1 + r}^n - 1}$

In this case:

$P = 1000$

$n = 4$

$r = \dfrac {8 \%} 2 = 4 \% = 0.04$

Hence:

$I = 1000 \paren {\paren {1 + 0 \cdotp 04}^4 - 1} \approx 1000 \times \paren {1 \cdotp 16985 - 1} = 169 \cdotp 85$

$\blacksquare$