Question

What is the difference between the. compound interests on Rs. $5,000$ for $1\frac{1}{2}$ years at $4\%$ per annum compounded yearly and half-yearly?

• A. Rs. $2.04$
• B. Rs. $3.06$
• C. Rs. $4.80$
• D. Rs. $8.30$

Answer 1

Answer: (A)

Rs. $2.04$

C.I when interest is compounded yearly
$=$ $[5000\times \left(1+\frac{4}{100}\right)\times (1+\frac{\frac{1}{2}\times 4}{100})]$
$=$ Rs. $\left(5000\times \frac{26}{25}\times \frac{51}{50}\right)$ $=$ Rs. $5,304$
C.I when interest is compounded half-yearly
$=$ Rs. $\left[5000\times {(1+\frac{2}{100})}^3\right]$
$=$ Rs. $\left(5000\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50}\right)$
$=$ Rs. $5,306.04$
$\therefore$ difference $=5306.04-5.304=2.04$