Question

Mr Dev purchased a car paying Rs $90,000$ and promised to pay Rs 5000 every 3 months for the next 10 years. The interest is $6$% p.a. compounded quarterly. If Mr Dev misses first 6 payments , how much should he pay at the time of 7th payment (approximately) to bring himself up to date.

• A. 36333
• B. 46532
• C. 56734
• D. 60322

Answer 1

The correct option is A 36333

$\Rightarrow$ We have $A=Rs.5000,n=7$ $I=\frac{6}{100}\times \frac{1}{4}=0.015$

$\Rightarrow$ At the time of 7th payment, equivalent amount of first 6 missed payment has also to be paid. Thus total payment to be made at the end of 7th period is the amount of annuity of 7 terms. Hence, amount required required to be paid is,

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

$\Rightarrow$ $M=\frac{5000}{0.015}\left[\right(1.015{)}^7-1]$ ----- ( 1 )

$\Rightarrow$ Let $x=(1.015{)}^7$

$\Rightarrow$ $logx=7log\left(1.015\right)$

$\Rightarrow$ $logx=7\left(0.0064\right)=0.0448$

$\Rightarrow$ $x=antilog\left(0.0448\right)$

$\Rightarrow$ $x=1.109$

Substitute value of $x$ in ( 1 ) we get,

$\Rightarrow$ $M=\frac{5000}{0.015}(1.109-1)$

$\Rightarrow$ $M=\frac{5000}{0.015}\times 0.109$

$\Rightarrow$ $M=\frac{5000\times 1000}{15}\times \frac{109}{1000}$

$\Rightarrow$ $M=Rs.36333.33\approx Rs.36333$