Question

Mr Dev purchased a car paying Rs $90,000$ and promising to pay Rs 5000 every 3 months for the next 10 years. The interest is $6$% p.a. compounded quarterly. If at the end of 5th year , he wants to finish his liability by a single payment , how much should he pay?

• A. 90100
• B. 80100
• C. 34504
• D. 54345

Answer 1

Answer: (A)

90100

$\Rightarrow$ We have $A=Rs.5000,I=\frac{6}{100}\times \frac{1}{4}=0.015$ and $n=20$

$\Rightarrow$ If at the end of 5th year, i.e., at the time of 20th payment, he wants to finish off the liability, then lump sum payment required is,

$\Rightarrow$ $5000$ + Present value of the remaining 20 installments.

$\Rightarrow$ $5000+V$

$\Rightarrow$ $5000$ + $\frac{A}{I}[1-(1+I{)}^{-n}]$

$\Rightarrow$ $5000+\frac{5000}{0.015}[1-(0.015{)}^{-20}]$ ---- ( 1 )

$\Rightarrow$ Let $x=(1.015{)}^{-20}$

$\Rightarrow$ $logx=-20log\left(1.015\right)$

$\Rightarrow$ $logx=-20\left(0.0064\right)=-0.128=\overline{1}.8720$

$\Rightarrow$ $x=antilog\left(\overline{1}.8720\right)=0.7447$

Substitute value of $x$ in ( 1 ),

$\Rightarrow$ $5000+\frac{5000}{0.015}(1-0.7447)$

$\Rightarrow$ $5000+\frac{5000}{0.015}\times 0.2553$

$\Rightarrow$ $Rs.90100$