Question

Find the difference between compound interest and simple interest on Rs. 12000 and in $1\frac{1}{2}$ years at 10% p.a. compounded yearly.

Answer 1

Given : P = Rs 12,000; n = $1\frac{1}{2}$ years and r = 10%

$S.I.=\frac{P\times R\times T}{100}=\frac{12,000\times 10\times \frac{3}{2}}{100}=Rs1,800$

To calculate C.I. For 1 year

P = Rs 12,000; n = 1 years and r = 10%

$C.I.=P{(1+\frac{r}{100})}^n=12,000{(1+\frac{10}{100})}^1=Rs13,200$

For next 1/2 year

P = Rs 13,200; n = 1/2 year and r = 10%

$C.I.=P{(1+\frac{r}{2\times 100})}^{2\times n}=13,200{(1+\frac{10}{2\times 100})}^{\frac{1}{2}\times n}$

$=13,200{\left(\frac{21}{20}\right)}^1$

= Rs 13,860

$\therefore$ C.I. = Rs 13,860 - Rs 12,000 = Rs 1,860

$\therefore$ Difference between C.I. and S.I.

= Rs 1,860 - Rs 1,800 = Rs 60