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Question

Find the amount and the compound interest on 50000 for $1 \frac{1}{2}$ years at 8% per annum, the interest is compounded semi-annually.

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Solution

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We have the formula for compound Interest,

$A = P (1 + \frac{r}{n})^{n . t}$

$A = T o t a l a m o u n t$
$P = P r i n c i p a l = 50000$
$r = a n n u a l i n t e r e s t r a t e = 8$ %
$n = n o . o f t i m e s c o m p o u n d e d p e r y e a r = 2$ , and $t = t i m e i n y e a r s = \frac{3}{2}$

Substituting, $A = 50000 (1 + \frac{0.08}{2})^{2 \times \frac{3}{2}}$

$A = 50000 (\frac{2.08}{2})^{3}$

$A = 56243.2$ This is the amount after $1$ and $\frac{1}{2}$ years

Compound Interest, $I = A - P = 56243.2 - 50000 = 6243.5$

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