Compound vs Simple Interest — Use 2-year difference to recover principal: For a certain principal, the difference between the 2-year compound interest and the 2-year simple interest at 8% per annum is ₹ 32. Find the principal.
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: ₹ 5000
Explanation
Introduction / Context:The difference between compound interest (CI) and simple interest (SI) over exactly two years at the same annual rate is a classic identity. It isolates the “extra” interest-on-interest that CI accumulates. This lets us back-solve the principal without separately knowing the amount.
Given Data / Assumptions:
- Annual rate r = 8% = 0.08
- Time t = 2 years
- CI − SI over 2 years = ₹ 32
- Principal P unknown
Concept / Approach:For two years at rate r (decimal), CI − SI = P * r^2. This follows from CI for 2 years = P[(1 + r)^2 − 1] = P(2r + r^2), SI for 2 years = P(2r), hence the difference is P r^2.
Step-by-Step Solution:
Use identity: CI − SI = P r^2.Substitute: 32 = P * (0.08)^2 = P * 0.0064.Solve P = 32 / 0.0064 = 5000.Verification / Alternative check:
Check numerically: On ₹ 5000, SI(2y, 8%) = 5000 * 0.16 = 800; CI(2y) adds r^2 * P = 0.0064 * 5000 = 32 more ⇒ 832. Difference 32 (matches).Why Other Options Are Wrong:
- ₹ 5250, ₹ 5550, ₹ 6000, ₹ 4800 do not satisfy 32 = P * 0.0064.
Common Pitfalls:
- Using r as “8” instead of 0.08 in the formula.
- Applying the identity to durations other than 2 years; it is specific to 2 years in this neat form.
Final Answer:₹ 5000.