Raghu wish to buy a laptop. He can buy it by paying 40,000 cash or by giving it in 10 installments as 4800 in the first month, 4750 in the second month, 4700 in the third month and so on. If he pays the money in this fashion, find (i) total amount paid in 10 installments. (ii) how much extra amount that he has to pay than the cost?
Solution :
By writing the installments as series, we get
4800 + 4750 + 4700 +.............to 10 installments
Sn = (n/2)[2a + (n - 1) d]
n = 10, a = 4800, d = 4750 - 4800 = -50
Sn = (n/2)[2a + (n - 1) d]
S10 = (10/2)[2(4800) + (10 - 1) (-50)]
= 5[9600 + 9(-50)]
= 5[9600 - 450]
= 5[9150]
= 45750
Extra amount paid by him = 45750 - 40000
= 5750