Question 3 of 4intermediate🔧 ApplyNumerical5 marks

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?

Correct Answer

The instalment scheme is better for Ali as it costs ₹ 24,800 compared to ₹ 25,440 under the loan option, saving him ₹ 640.

Exercise: EXERCISE A2.2 | Q: 3 | (Page Page 9-10)
For More Understanding

Explanation

This problem requires comparing two financing options. In the instalment scheme, we calculate the effective interest rate by considering the reducing balance of principal each month. The total interest paid is the difference between total instalments and the balance amount. For the society loan, simple interest is calculated on the borrowed amount for 6 months. The comparison shows that the instalment scheme charges an effective rate of approximately 17.78% per annum, which is lower than the society's 18% per annum.

Solution Steps

  1. Step 1: Calculate total payment under Instalment Scheme Cash price = ₹ 24,000 Cash down payment = ₹ 8,000 Balance = ₹ 24,000 - ₹ 8,000 = ₹ 16,000 Total instalments = 6 × ₹ 2,800 = ₹ 16,800 Interest paid = ₹ 16,800 - ₹ 16,000 = ₹ 800 Total payment = ₹ 8,000 + ₹ 16,800 = ₹ 24,800

  2. Step 2: Find effective rate of interest under instalment scheme 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 Sum of principals = ₹ 54,000 Interest = (Sum of principals × Rate) / (12×10012 \times 100) 800 = (54,000 × r) / 1200 r = 17.78% per annum (approximately)

  3. Step 3: Calculate total payment under Loan from Society Loan amount = ₹ 16,000 Rate = 18% per annum Time = 6 months = ½ year Interest = (16,000×18000 \times 18 × ½) / 100 = ₹ 1,440 Total payment = ₹ 8,000 + ₹ 16,000 + ₹ 1,440 = ₹ 25,440

  4. Step 4: Compare both options Instalment scheme total = ₹ 24,800 Loan option total = ₹ 25,440 Difference = ₹ 25,440 - ₹ 24,800 = ₹ 640

    Since ₹ 24,800 < ₹ 25,440, the instalment scheme is better for Ali.

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