Mathematics for FinancePYQ Dec 22Question 1240 of 512
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A sum of money invested compound interest double itself in four years. In how many years it become 32\displaystyle 32 times of itself at the same rate of compound interest?

Options

A12 years
B16 years
C20 years
D24 years
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Correct Answer

✅ Option c — 20 years

All Options:

  • A12 years
  • B16 years
  • C20 years
  • D24 years

Detailed Solution & Explanation

**Derivation of Compounding Period to become 32 Times** Given: - A sum doubles itself in 4\displaystyle 4 years under Compound Interest. A4=P(1+r)4=2P  ⟹  (1+r)4=2A_4 = P(1 + r)^4 = 2P \implies (1 + r)^4 = 2 **Step 1: Set up the equation for the sum to become 32 times itself** At=P(1+r)t=32P  ⟹  (1+r)t=32A_t = P(1 + r)^t = 32P \implies (1 + r)^t = 32 **Step 2: Express 32 as a power of 2** 32=2532 = 2^5 **Step 3: Substitute 2=(1+r)4\displaystyle 2 = (1 + r)^4** (1+r)t=[(1+r)4]5(1 + r)^t = \left[(1 + r)^4\right]^5 (1+r)t=(1+r)20  ⟹  t=20 years(1 + r)^t = (1 + r)^{20} \implies t = 20 \text{ years} Hence, **Option C** is the correct answer.

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