A T.V. can be purchased for ₹ 24000 cash or for ₹ 8000 cashdown payment and six monthly instalments of ₹ 2800 each. Ali goes to market to buy a T.V., and he has ₹ 8000 with him. He has now two options. One is to buy TV under instalment scheme or to make cash payment by taking loan from some financial society. The society charges simple interest at the rate of 18% per annum simple interest. Which option is better for Ali?
The instalment scheme is better for Ali as it charges approximately 17.78% rate of interest, which is lower than the 18% charged by the financial society.
Explanation
This problem requires comparing the effective interest rate charged by the instalment scheme with the rate charged by the financial society. Following the methodology from Example 2 in the textbook, we calculate the principal for each month by subtracting the instalment amount from the previous month's balance. The sum of these monthly principals is used with the simple interest formula to find the rate charged by the shopkeeper. Since the entire payment is completed within one year, simple interest applies.
Solution Steps
Step 1: Calculate interest paid in instalment scheme Cash price of TV = ₹ 24,000 Cash down payment = ₹ 8,000 Balance to be paid = ₹ 24,000 - ₹ 8,000 = ₹ 16,000 Total paid in instalments = 6 × ₹ 2,800 = ₹ 16,800 Interest paid = ₹ 16,800 - ₹ 16,000 = ₹ 800
Step 2: Calculate principal for each month Principal for 1st month = ₹ 16,000 Principal for 2nd month = ₹ 16,000 - ₹ 2,800 = ₹ 13,200 Principal for 3rd month = ₹ 13,200 - ₹ 2,800 = ₹ 10,400 Principal for 4th month = ₹ 10,400 - ₹ 2,800 = ₹ 7,600 Principal for 5th month = ₹ 7,600 - ₹ 2,800 = ₹ 4,800 Principal for 6th month = ₹ 4,800 - ₹ 2,800 = ₹ 2,000
Step 3: Find the rate of interest in instalment scheme Sum of monthly principals = ₹ 16,000 + ₹ 13,200 + ₹ 10,400 + ₹ 7,600 + ₹ 4,800 + ₹ 2,000 = ₹ 54,000 Using simple interest formula: Interest = (Sum of monthly principals × r) / () ₹ 800 = (₹ 54,000 × r) / 1200 r = (₹ ) / ₹ 54,000 = 17.78% (approximately)
Step 4: Compare and conclude Rate charged by instalment scheme 17.78% p.a. Rate charged by financial society = 18% p.a. Since 17.78% < 18%, the instalment scheme is better for Ali.