Find the difference between simple interest and compound interest on Rs 16000 for 1.5 rears or 3/2 years at 5 % per annum ,compound interest being reckoned half yearly.

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Solution:

⇨Given
⇨p=16000
⇨r=5 %
⇨n=1.5 annul for S.I.
⇨The simple interest will be

$\large S.I=\frac{p\times r\times n}{100}$

$\large \Rightarrow S.I=\frac{16000\times 5\times 1\frac{1}{2}}{100}$

$\large \Rightarrow S.I=\frac{80000\times \frac{3}{2}}{100}$

$\large \Rightarrow S.I=800\times \frac{3}{2}$

$\large \Rightarrow S.I=400\times 3$

$\large \Rightarrow S.I=1200$ Rs

⇨Given
⇨p=16000
⇨r=5 %
⇨n=1.5 Half-yearly for C.I

⇨The compound interest will be

$\large C.I=p\left \{ \left ( 1+\frac{r}{2\times 100} \right )^{2n}-1 \right \}$ $\large \Rightarrow C.I=16000\left \{ \left ( 1+\frac{5}{200} \right )^{2\times 1\frac{1}{2}}-1 \right \}$

$\large \Rightarrow C.I=16000\left \{ \left ( \frac{200+5}{200} \right )^{2\times \frac{3}{2}}-1 \right \}$ $\large \Rightarrow C.I=16000\left \{ \left ( \frac{205}{200} \right )^{3}-1 \right \}$

$\large \Rightarrow C.I=16000\left \{ \frac{8615125}{8000000}-1 \right \}$ $\large \Rightarrow C.I=16000\left \{ \frac{8615125-8000000}{8000000} \right \}$