Definition:Interest/Compound

Definition

Compound interest is interest which is calculated by:

adding the interest which has accrued on the principal

calculating the interest on the sum

at the end of agreed conversion periods.

Such interest is said to be compounded according to that conversion period.

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 $\pounds 169 \cdotp 85$.