Mathematics for FinanceMTP Dec 23 Series IQuestion 1398 of 512
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A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as 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** Given: - A sum of money doubles itself (A=2P\displaystyle A = 2P) in 4\displaystyle 4 years under Compound Interest. (1+r)4=2(1 + r)^4 = 2 **Step 1: Set up the equation for the sum to become 32 times itself (A=32P\displaystyle A = 32P)** (1+r)t=32(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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