Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
Amount Paid to buy scooter = Rs. 22,000
Shamshad Pays Cash = Rs. 4000
Remaining Balance = Rs. (22000 - 4000) = 18000
Annual Instalment = Rs 1000 + interest@10% on unpaid amount
1st Instalment
Unpaid Amount = Rs. 18000
Interest on Unpaid Amount = (10/100) × 18000 = 1800
Amount of Instalment = Rs. 1000 + Rs. 1800 = Rs. 2800
2nd Instalment
Unpaid Amount = Rs. (18000 - 1000) = Rs. 17000
Interest on Unpaid Amount = (10/100) × 17000 = 1700
Amount of Instalment = Rs. 1000 + Rs. 1700 = Rs. 2700
3rd Instalment
Unpaid Amount = Rs. (17000 - 1000) = Rs. 16000
Interest on Unpaid Amount = (10/100) × 16000 = 1600
Amount of Instalment = Rs. 1000 + Rs. 1600 = Rs. 2600
Total no. of Instalments = 18000/1000 = 18
Thus, Annual Instalments are 2800, 2700, 2600, …upto 18 terms
Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.
Here
first term(a) = 2800
Common difference(d) = 2700 - 2800 = - 100
Number of terms(n) = 18
Total amount paid in 12 instalments is given by -
Sn = (n/2)[2a + (n - 1)d]
∴ S18 = (18/2)[2(2800) + (18 - 1)( - 100)]
= 9[5600 + 17( - 100)]
= 9[5600 - 1700]
= 9 × 3900
= 35100
Hence, total amount paid in 12 Instalments = Rs 35100
Hence,
Total Cost of Tractor
= Amount paid earlier + Amount paid in 12 Instalments
= Rs. (4000 + 35100)
= Rs. 39100