3. 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?

Understand the Question Ali has ₹ and needs to choose between two payment methods for a ₹ TV: Option 1 (Instalment Scheme): Pay ₹ down payment plus monthly instalments of ₹ . Option 2 (Loan Scheme): Pay ₹ from his cash and take a loan of the remaining ₹ for months at simple interest per annum. To find the better option, we calculate and compare the total cost paid by Ali in each scheme. Step 1 · Calculate Cost of Instalment Scheme Given cashdown payment and monthly instalments of ₹ each. Total cost under instalment scheme . Step 2 · Calculate Cost of Loan Scheme Ali pays his ₹ in cash and borrows the remaining amount as a loan. Loan period and rate Total cost under loan scheme . Step 3 · Compare the Options Comparing the two options: Total cost in Instalment Scheme Total cost in Loan Scheme Since , the instalment scheme costs less. Answer > The instalment scheme is better for Ali. Common Mistakes Time Unit Error: Forgetting to convert the loan period from months to years () before substituting into the simple interest formula. Incorrect Principal: Calculating simple interest on the entire cash price (₹ ) instead of only the borrowed principal amount (₹ ).

Appendix 2: Mathematical Modelling | A2.2

Question 3

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?

Solution

Understand the Question

Ali has ₹ $8000$ $8000$ and needs to choose between two payment methods for a ₹ $24000$ $24000$ TV:
- Option 1 (Instalment Scheme): Pay ₹ $8000$ down payment plus $6$ monthly instalments of ₹ $2800$ .
- Option 2 (Loan Scheme): Pay ₹ $8000$ from his cash and take a loan of the remaining ₹ $16000$ for $6$ months at $18\%$ simple interest per annum.
To find the better option, we calculate and compare the total cost paid by Ali in each scheme.

Step 1 · Calculate Cost of Instalment Scheme

Given cashdown payment $= ₹ 8000$ and $6$ monthly instalments of ₹ $2800$ each. Diagram 1

\begin{aligned} \text{Total instalment amount} &= 6 \times 2800 \\[0.6em] &= 16800 \end{aligned}

\begin{aligned} \text{Total cost} &= \text{Cashdown payment} + \text{Total instalment amount} \\[0.6em] &= 8000 + 16800 \\[0.6em] &= 24800 \end{aligned}

Total cost under instalment scheme $= ₹ 24800$ .

Step 2 · Calculate Cost of Loan Scheme

Ali pays his ₹ $8000$ in cash and borrows the remaining amount as a loan.

\begin{aligned} \text{Principal } (P) &= \text{Cash price} - \text{Cash Ali has} \\[0.6em] &= 24000 - 8000 \\[0.6em] &= 16000 \end{aligned}

Loan period $T = 6 \text{ months} = \dfrac{6}{12} \text{ years} = 0.5 \text{ years}$ and rate $R = 18\% \text{ p.a.}$

\begin{aligned} \text{Simple Interest (SI)} &= \dfrac{P \times R \times T}{100} \\[0.6em] &= \dfrac{16000 \times 18 \times 0.5}{100} \\[0.6em] &= \dfrac{16000 \times 9}{100} \\[0.6em] &= 160 \times 9 \\[0.6em] &= 1440 \end{aligned}

\begin{aligned} \text{Total cost} &= \text{Cash price} + \text{Simple Interest} \\[0.6em] &= 24000 + 1440 \\[0.6em] &= 25440 \end{aligned}

Total cost under loan scheme $= ₹ 25440$ .

Step 3 · Compare the Options

Comparing the two options:

Total cost in Instalment Scheme $= ₹ 24800$
Total cost in Loan Scheme $= ₹ 25440$

Since $₹ 24800 < ₹ 25440$ , the instalment scheme costs less.

Answer

The instalment scheme is better for Ali.

Common Mistakes

Time Unit Error: Forgetting to convert the loan period from months to years ( $T = \dfrac{6}{12} = 0.5\text{ years}$ ) before substituting into the simple interest formula.
Incorrect Principal: Calculating simple interest on the entire cash price (₹ $24000$ ) instead of only the borrowed principal amount (₹ $16000$ ).

Question 3

More questions in A2.2