Mathematics for FinanceMTP Jun 23 Series IQuestion 1379 of 512
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A sum of money invested of 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\displaystyle 12 years
B16\displaystyle 16 years
C20\displaystyle 20 years
D18\displaystyle 18 years
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Correct Answer

✅ Option c — 20\displaystyle 20 years

All Options:

  • A12\displaystyle 12 years
  • B16\displaystyle 16 years
  • C20\displaystyle 20 years
  • D18\displaystyle 18 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 2: 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 3: Express 32 as a power of 2** 32=2532 = 2^5 **Step 4: 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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