Question

The difference between simple interest and compound interest on Rs. $1200$ for one year at $10\%$ per annum. Reckoned half yearly is

• A. Rs. $2.50$
• B. Rs. $3$
• C. Rs. $3.75$
• D. Rs. $4$

Answer 1

Answer: (B)

Rs. $3$

Given, $P=$ Rs. $1200,R=10\%$ p.a., $T=1$ years

$\therefore S.I.=\frac{P\times R\times T}{100}=\frac{1200\times 10\times 1}{100}$ = Rs. $120$
For C.I. reckoned half yearly, $P=$ Rs. $1200,r=5\%$ per half year, $n=2$ half year
$\therefore$ C.I. $=$ Rs. $(1200{(1+\frac{5}{100})}^2-1200)$ $=$ Rs. $\left(\right(1200\times \frac{21}{20}\times \frac{21}{20})-1200)$
$=$ Rs. $1323-$ Rs. $1200=$ Rs. $123$

$\therefore$ Required difference $=$ Rs. $123-$ Rs. $120=$ Rs. $3$