Question

What is the difference between the compound interests on $Rs.5000$ 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

The correct option is A $Rs.2.04$

C.I. when interest compounded yearly $=Rs.[5000\times (1+\frac{4}{100})\times (1+\frac{\frac{1}{2}\times 4}{100})]$
$=Rs.(5000\times \frac{26}{25}\times \frac{51}{50})$
$=Rs.5304$.
C.I. when interest is compounded half-yearly $=Rs.[5000\times {(1+\frac{2}{100})}^2]$
$=Rs.(5000\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50})$
$=Rs.5306.04$
$\therefore Difference=Rs.(5306.04-5304)=Rs.2.04$