A computer is available for ₹ 39000 cash or ₹ 17000 as cash down payment followed by five monthly instalments of ₹ 4800 each. What is the rate of interest under the instalment plan? (M.A.T., 2006)

### Concept & Formula The rate of interest in an instalment scheme can be found by calculating the total interest paid and equating it to the interest generated by the sum of the monthly outstanding balances. $$R = \frac{I \times 100 \times 12}{\text{Sum of Outstanding Balances} \times 1}$$ ### Step-by-Step Solution * **Given:** Cash Price = ₹ 39,000, Down Payment = ₹ 17,000. * Balance to be paid = $39,000 - 17,000$ = ₹ 22,000. * Total amount paid in 5 instalments = $5 \times 4800$ = ₹ 24,000. * Total Interest (I) = $24,000 - 22,000$ = ₹ 2,000. * **Calculation:** Find the outstanding principal for each of the 5 months by subtracting the instalment amount from the previous balance: * Month 1: ₹ 22,000 * Month 2: $22,000 - 4800$ = ₹ 17,200 * Month 3: $17,200 - 4800$ = ₹ 12,400 * Month 4: $12,400 - 4800$ = ₹ 7,600 * Month 5: $7,600 - 4800$ = ₹ 2,800 * Sum of outstanding balances = $22000 + 17200 + 12400 + 7600 + 2800$ = ₹ 62,000. * Now, apply the simple interest formula for 1 month ($T = \frac{1}{12}$ year): $$2000 = \frac{62000 \times R \times 1}{100 \times 12}$$ * $R = \frac{2000 \times 1200}{62000} = \frac{2400}{62} \approx 38.709\%$ ### Exam Strategy & Shortcut To quickly find the sum of outstanding balances, note it's an AP: $a = 22000$, $d = -4800$. Sum = $\frac{n}{2}[2a + (n-1)d] = \frac{5}{2}[44000 - 19200] = 2.5 \times 24800 = 62000$. ### Common Pitfall Students often subtract the principal component of the instalment instead of the full instalment amount when determining the outstanding balance each month. In real-world flat rate SI problems, the full instalment is subtracted. ### Final Answer Therefore, the correct answer is **38.71% p.a.**.