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
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B
235467
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C
228467
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D
None of these
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Solution
The correct option is B 238467 ⇒ We have, A=Rs.5000,n=40 and I=6100×14=0.015
⇒V=AI[1−(1+I)−n]
⇒V=50000.015[1−(1+0.015)−40] --- ( 1 )
⇒ Let x=(1.015)−40
⇒logx=−40(0.0064)
⇒logx=−0.256=(¯1.7440)
⇒x=antilog(¯1.7440)
⇒x=0.5546
Substitute this value in ( 1 ),
⇒V=50000.015(1−0.5546)
⇒V=50000.015×0.4454=Rs.148466.67
∴ Total cash value of the car = Rs.90000+Rs.148466.67