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 $15$ years interest compounded annually.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $45$ years

All Options:

  • A$42$ years
  • B$43$ years
  • C$45$ years
  • D$46$ years

Detailed Solution & Explanation

**Derivation of Compounding Period** Given: - A sum of money doubles itself (A=2P\displaystyle A = 2P) in $15$ 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  years\displaystyle \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

Exam Strategy Tip

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