Question

Kumar buys a maruti car for Rs. 2,40,000 at a down payment of Rs. 1,20,000 and the rest annual instalments of Rs. 10,000 pluse 12% interest on the unpaid amount. Eventually what will the car cost him?

Answer 1

Given that, Kumar pays Rs. 120000 in cash.
Therefore, unpaid amount = Rs. 240000 - Rs. 120000 = Rs. 120000
According to the given condition, the interest paid annually is 12% of 120000, 12% of 110000, 12% of 100000,...,12% of 10000
Thus, total interest to be paid = 12% of 120000 + 12% of 110000 + 12% of 100000 + ....+ 12% of 10000
= 12% of (120000 + 110000 + 100000 +...+ 10000)
= 12% of (10000 + 20000 + 30000 +...+ 120000)
Now, the series 10000, 20000, 30000...120000 is an A.P. with both the first term and common difference equal to 10000.
Let the number of terms of the A.P. be $n$.
120000 = 10000 + ($n$ - 1) 10000
Implies, 1 + ($n$ - 1) = 12
implies, $n$ = 12
Sum of the A.P.
= 12[2(10000) + (12-1)(10000)]/2
= 6[20000 + 110000]
= 780000
Thus, total interest to be paid = 12% of (10000 + 20000 + 30000 +...+ 120000)
= 12% of 780000 = 93600
Thus, cost of car = (Rs. 240000 + Rs. 93600)
= Rs. 333600