Question:
Raghav buys a shop for 120000 Rs. he pays half of the amount in cash and agrees to pay the balance in 12 annuals instalments of Rs 5000 each . if the rate of interest is 12% and he pays with instalment the interest due on the unpaid amount, find the total cost of the shop.
Answer:
Given, Raghav buys a shop for Rs 120000
Now, amount paid by Raghav in cash = 120000/2 = Rs 60000
So, balance amount to be paid in installments = 120000 - 60000 = 60000
Given, amount of each installment = 5000
Now, amount of the first installment = 5000 + interest paid on unpaid amount 60000
= 5000 + (60000*12*1)/100
= 5000 + 600*12
= 5000 + 7200
= 12200
Amount of the second installment = 5000 + interest paid on unpaid amount 55000 (60000 - 5000)
= 5000 + (55000*12*1)/100
= 5000 + 550*12
= 5000 + 6600
= 11600
Amount of the third installment = 5000 + interest paid on unpaid amount 50000 (55000 - 5000)
= 5000 + (50000*12*1)/100
= 5000 + 500*12
= 5000 + 6000
= 11000
So, amount paid for installment is
12200, 11600, 11000.........up to 12
This form an AP
Now, first term a = 12200
Common difference d = 11600 - 12200 = -600
Number of terms n = 12
Now, total cost of the shop = 60000 + sum of 12 installment
= 60000 + (12/2)*{2*12200 + (12 - 1)*(-600)}
= 60000 + 6*{24400 - 11*600}
= 60000 + 6 *{24400 - 6600}
= 60000 + 6 * 17800
= 60000 + 106800
= 166800
So, total cost of the shop is Rs. 166800
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