Mathematics of FinanceMCQMTP Mar 22Question 1346 of 512
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The time in by which a sum of money is 8\displaystyle 8 times of itself if it doubles itself in 15\displaystyle 15 years interest compounded annually.

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

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Detailed Solution & Explanation

**Derivation of Compounding Period** Given: - A sum of money doubles itself (A=2P\displaystyle A = 2P) in 15\displaystyle 15 years under Compound Interest. (1+r)15=2(1 + r)^{15} = 2 **Step 1: Set up the equation for the sum to become 8 times itself (A=8P\displaystyle A = 8P)** (1+r)t=8(1 + r)^t = 8 **Step 2: Express 8 as a power of 2** 8=238 = 2^3 **Step 3: Substitute 2=(1+r)15\displaystyle 2 = (1 + r)^{15}** (1+r)t=[(1+r)15]3(1 + r)^t = \left[(1 + r)^{15}\right]^3 (1+r)t=(1+r)45  ⟹  t=45 years(1 + r)^t = (1 + r)^{45} \implies t = 45 \text{ years} Hence, **Option C** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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