Question

A man borrows Rs $37500$ and agrees to repay in semi-annual installments of Rs $2250$ each, the first due in $6$ months. How many payments must he make if rate of interest is $6\%$ compounded semi-annually?

• A. $23$
• B. $24$
• C. $25$
• D. $22$

Answer 1

Answer: (B)

$24$

$\Rightarrow$ Here, we have to find the number of payments, $n$.

$\Rightarrow$ $V=Rs.37500$ and $A=Rs.2250$

$\Rightarrow$ Rate of interest compounded semi-annually = $\frac{1}{2}\times 6\%=\frac{1}{2}\times \frac{6}{100}=0.03$

$\Rightarrow$ $V=\frac{A}{r}\times [1-(1+r{)}^{-n}]$

$\Rightarrow$ $37500=\frac{2250}{0.03}\times [1-(1.03{)}^{(-n)}]$

$\Rightarrow$ $1-(1.03{)}^{-n}=\frac{37500\times 0.03}{2250}$

$\Rightarrow$ $(1.03{)}^{(-n)}=0.5$

$\Rightarrow$ $-nlog\left(1.03\right)=log\left(0.5\right)$

$\Rightarrow$ $-n\left(0.0128\right)=-0.3010$

$\Rightarrow$ $n=\frac{-0.3010}{-0.0128}$

$\therefore$ $n=23.51\approx 24$