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 results in a total payment of ₹ 24800, which is ₹ 640 less than the loan option (₹ 25440).

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

Explanation

This problem from the NCERT textbook on Mathematical Modelling requires comparing two payment options. Following the methodology shown in Example 2 (Juhi's bicycle problem), students must calculate the effective interest rate in the instalment scheme and compare it with the society's rate of 18% p.a. The instalment scheme charges approximately 17.78% p.a., which is lower than 18% p.a., making it the better option.

Solution Steps

  1. Step 1: Calculate total payment under Instalment Scheme Cash down payment = ₹ 8000 6 monthly instalments of ₹ 2800 each = 6 × ₹ 2800 = ₹ 16800 Total payment = ₹ 8000 + ₹ 16800 = ₹ 24800

  2. Step 2: Calculate interest charged in Instalment Scheme Cash price of TV = ₹ 24000 Balance to be paid = ₹ 24000 - ₹ 8000 = ₹ 16000 Total paid in instalments = ₹ 16800 Interest paid = ₹ 16800 - ₹ 16000 = ₹ 800

  3. Step 3: Find effective rate of interest in Instalment Scheme Principal for 1st month = ₹ 16000 Principal for 2nd month = ₹ 16000 - ₹ 2800 = ₹ 13200 Principal for 3rd month = ₹ 13200 - ₹ 2800 = ₹ 10400 Principal for 4th month = ₹ 10400 - ₹ 2800 = ₹ 7600 Principal for 5th month = ₹ 7600 - ₹ 2800 = ₹ 4800 Principal for 6th month = ₹ 4800 - ₹ 2800 = ₹ 2000 Sum of principals = ₹ 16000 + ₹ 13200 + ₹ 10400 + ₹ 7600 + ₹ 4800 + ₹ 2000 = ₹ 54000

  4. Step 4: Calculate rate of interest This sum represents principal for 1 month. Interest = ₹ 800, Principal = ₹ 54000, Time = 1/12 year Using SI = P × r × t / 100: 800 = 54000 × r × (1/12) / 100 800 = 45 × r r = 800/45 ≈\approx 17.78% per annum

  5. Step 5: Calculate total payment under Loan Option Loan amount needed = ₹ 16000 Interest for 6 months = 16000×1816000 \times 18 × (6/12) / 100 = ₹ 1440 Total repayment = ₹ 16000 + ₹ 1440 = ₹ 17440 Total outflow = ₹ 8000 (Ali's money) + ₹ 17440 = ₹ 25440

  6. Step 6: Compare both options Instalment Scheme total = ₹ 24800 Loan Option total = ₹ 25440 Difference = ₹ 25440 - ₹ 24800 = ₹ 640

    Since 17.78% < 18% and ₹ 24800 < ₹ 25440, the instalment scheme is better for Ali.

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