Question

The difference between compound interest and simple interest on a sum for $2$ years at $10\%$ per annum, when the interest is compounded annually is Rs. $16$. If the interest were compounded half yearly, the difference in two interests would be

• A. $Rs.36.91$
• B. $Rs.24.81$
• C. $Rs.32.41$
• D. $Rs.31.61$

Answer 1

Answer: (B)

For first year, $S.I.=C.I$.
Now, Rs. $16$ is the $S.I$. on $S.I$. for $1$ year.
$\therefore$ Rs. $10$ is S.I. on Rs. $100$
$\therefore$ Rs. $16$ is $S.I$. on $(\frac{100}{10}\times 16)=$ Rs. $160$
$\therefore$ S.I. on principal for $1$ year at $10\%$ is Rs. $160$.
$\therefore$ Principal $=\left(\frac{100\times 160}{10\times 1}\right)=$ $Rs.1600$.
Amount for 2 years compounded half yearly
$=Rs.[1600\times {(1+\frac{5}{100})}^4]=Rs.1944.81$
$\therefore$ $C.I.Rs(1944.81-1600)=Rs.344.81$
$S.I.=Rs.\left(\frac{1600\times 10\times 2}{100}\right)=Rs.320$
$\therefore (C.I.)-(S.I.)=Rs.(344.81-320)=Rs.24.81$