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Raghav buys a shop for Rs 1,20,000. He pays half of the amount in cash and agrees to pay the balance in 12 annual instalments of Rs 5000 each. If the rate of interest is 12 percent and he pay with the instalments the interest due on the unpaid amount, find the total cost of the shop.

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Rs. 166800

Rs. 254301

Rs. 354112

Rs. 412001

answer is A.

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Detailed Solution

Given,
Cost price of shop = 120000.
Amount he paid in cash is ½ of it. Thus, the reaming amount will be half of actual price.,

P = \frac{1}{2} \times 120000

P = 60000

Given that amount of each installment
= 5000.
Amount of first installment with 12% interest,

= 5000 + 12 / 100 \times 60000

= 5000 + 600 \times 12

= 5000 + 7200

= 12200

Amount of second installment,

= 5000 + 12 / 100 \times (60000 - 5000)

= 5000 + \frac{12}{100} \times 55000

= 5000 + 550 \times 12

= 5000 + 6600

= 11600

Similarly, he pays 12 installment which follow arithmetic progression as 12200, 11600.......
Here,
First term a= 12200
Common different d = 11600 – 12200

= - 600

Total terms n = 12.
Thus, sum of series,

S_{n} = \frac{n}{2} (2 a + (n - 1) \times d)

S_{12} = 6 (24400 - 6600)

Total cost of the soap,

= 60000 + 6 (24400 - 6600)

= 60000 + 6 \times 17800

= 60000 + 106800

= 166800

Correct option is 1.

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