Equal Annual Instalments under Compound Interest — Two-year repayment at 20%: A loan of ₹ 550 is to be repaid in two equal annual instalments with 20% compound interest per annum. Find the value of each instalment.
Aptitude
Compound Interest
Difficulty: Medium
Choose an option
Answer
Correct Answer: Rs. 360
Explanation
Introduction / Context:Equal-instalment repayment under compound interest uses time-value equivalence: the present value of all instalments discounted at the loan rate equals the principal borrowed. For annual instalments over two years at rate i, PV = A/(1 + i) + A/(1 + i)^2. Set this equal to the principal and solve for A (the instalment size).
Given Data / Assumptions:
- Principal P = ₹ 550
- Annual rate i = 20% = 0.20
- Two equal end-of-year instalments = A each
Concept / Approach:Present value equation: 550 = A/(1.2) + A/(1.2)^2. Compute the discount sum, then isolate A. This avoids stepwise amortization while yielding the exact same result.
Step-by-Step Solution:
Compute discount factors: 1/1.2 ≈ 0.833333..., 1/1.2^2 ≈ 0.694444...Sum ≈ 0.833333... + 0.694444... = 1.527777...Solve A = 550 / 1.527777... = ₹ 360 (exact).Verification / Alternative check:
Amortization route gives same A: After first year, 550*1.2 − 360 = 300; after second, 300*1.2 − 360 = 0.Why Other Options Are Wrong:
- ₹ 421, ₹ 396, ₹ 350, ₹ 380 do not satisfy the PV equality at 20% for two periods.
Common Pitfalls:
- Discounting at 20 (instead of 0.20) or forgetting the second discount.
Final Answer:Rs. 360.