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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
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B
80100
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C
34504
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D
54345
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Solution

The correct option is C 90100
We have A=Rs.5000,I=6100×14=0.015 and n=20
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,
5000 + Present value of the remaining 20 installments.
5000+V
5000 + AI[1(1+I)n]

5000+50000.015[1(0.015)20] ---- ( 1 )

Let x=(1.015)20
logx=20log(1.015)
logx=20(0.0064)=0.128=¯1.8720
x=antilog(¯1.8720)=0.7447
Substitute value of x in ( 1 ),
5000+50000.015(10.7447)

5000+50000.015×0.2553

Rs.90100

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