Compound Interest – Repeated doublings: amount after 20 years when it doubles in 5 years: A sum of ₹ 2,400 deposited at compound interest doubles in 5 years. What will it become after 20 years?

Introduction / Context:
If a deposit doubles in a fixed number of years at a constant compound rate, then over multiples of that period the amount multiplies by corresponding powers of 2. No explicit rate is necessary so long as the doubling interval is consistent over time.

Given Data / Assumptions:

• Initial amount P = 2,400
• Doubling time = 5 years
• Total time of interest = 20 years
• Constant compounding rate throughout

Concept / Approach:
Since 20 years is four times 5 years, the amount experiences four doublings. Each doubling multiplies by 2, so overall factor = 2^4 = 16. Final amount = 2,400 * 16 = 38,400.

Step-by-Step Solution:
Number of doublings = 20 / 5 = 4Overall multiplier = 2^4 = 16Final amount A = 2,400 * 16 = 38,400

Verification / Alternative check:
Track progression: 2,400 → 4,800 (5 yr) → 9,600 (10 yr) → 19,200 (15 yr) → 38,400 (20 yr). The sequence confirms the calculation.

Why Other Options Are Wrong:
₹ 24,000 corresponds to only three doublings from 3,000; ₹ 19,200 is the 15-year value (three doublings from 2,400). “Cannot be determined” is incorrect because the constant doubling interval suffices to compute the 20-year amount.

Common Pitfalls:
Confusing simple with compound interest can lead to linear scaling; remember that compounding induces exponential growth, and knowing the doubling time is enough to project to multiples thereof.

Final Answer:
₹ 38,400