Mathematics for FinanceMTP June 24 Series IIQuestion 1539 of 512
All Questions

The time by which a sum of money is 8\displaystyle 8 times of itself if it doubles itself in 15\displaystyle 15 years.

Options

A42\displaystyle 42 years
B43\displaystyle 43 years
C45\displaystyle 45 years
D46\displaystyle 46 years
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Correct Answer

✅ Option c — 45\displaystyle 45 years

All Options:

  • A42\displaystyle 42 years
  • B43\displaystyle 43 years
  • C45\displaystyle 45 years
  • D46\displaystyle 46 years

Detailed Solution & Explanation

Let the initial principal amount be P\displaystyle P. The principal doubles itself in 15\displaystyle 15 years under compound interest. A=P(1+i)15=2P  ⟹  (1+i)15=2A = P(1+i)^{15} = 2P \implies (1+i)^{15} = 2 We want to find the time n\displaystyle n for the principal to become 8\displaystyle 8 times itself: 8P=P(1+i)n  ⟹  8=(1+i)n8P = P(1+i)^n \implies 8 = (1+i)^n Since 8=23\displaystyle 8 = 2^3: 23=(1+i)n2^3 = (1+i)^n Substituting 2=(1+i)15\displaystyle 2 = (1+i)^{15}: [(1+i)15]3=(1+i)n\left[(1+i)^{15}\right]^3 = (1+i)^n (1+i)45=(1+i)n  ⟹  n=45 years(1+i)^{45} = (1+i)^n \implies n = 45 \text{ years} Hence, **Option C** is the correct answer.

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