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. What is the cash value (approximately) of the car ?

• A. 238467
• B. 235467
• C. 228467
• D. None of these

Answer 1

Answer: (A)

238467

$\Rightarrow$ We have, $A=Rs.5000,n=40$ and $I=\frac{6}{100}\times \frac{1}{4}=0.015$

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

$\Rightarrow$ $V=\frac{5000}{0.015}[1-(1+0.015{)}^{-40}]$ --- ( 1 )

$\Rightarrow$ Let $x=(1.015{)}^{-40}$

$\Rightarrow$ $logx=-40\left(0.0064\right)$

$\Rightarrow$ $logx=-0.256=\left(\overline{1}.7440\right)$

$\Rightarrow$ $x=antilog\left(\overline{1}.7440\right)$

$\Rightarrow$ $x=0.5546$

Substitute this value in ( 1 ),

$\Rightarrow$ $V=\frac{5000}{0.015}(1-0.5546)$

$\Rightarrow$ $V=\frac{5000}{0.015}\times 0.4454=Rs.148466.67$

$\therefore$ Total cash value of the car = $Rs.90000+Rs.148466.67$

$\Rightarrow$ Total cash value of car = $Rs.2,38,467$ approx.