Question

Determine the rate of interest at which a sum of money will become $\frac{216}{125}$ times the original amount in $1\frac{1}{2}$ years, if the interest is compounded half-yearly.

• A. $20\%$
• B. $30\%$
• C. $40\%$
• D. $10\%$

Answer 1

Answer: (C)

$40\%$

Amount $=\frac{216}{125}P$, $T=1.5$, $R=?$

for $CI$ half yearly

Amount $=P{(1+\frac{R}{200})}^{2T}=\frac{216}{125}P$

$⟹{(1+\frac{R}{200})}^3=\frac{216}{125}$

$=(1+\frac{R}{200})=\frac{6}{5}⟹R=40\%$