Mathematics of FinanceMCQPYQ Nov 19Question 1298 of 512
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A sum of money doubles itself at compound interest in 10\displaystyle 10 years. In how many years will it become eight times?

Options

A20\displaystyle 20
B30\displaystyle 30
C40\displaystyle 40
D35\displaystyle 35
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Correct Answer

Option b30\displaystyle 30

All Options:

  • A20\displaystyle 20
  • B30\displaystyle 30
  • C40\displaystyle 40
  • D35\displaystyle 35

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Detailed Solution & Explanation

**Derivation of Compounding Period** Given: - A sum of money doubles itself (A=2P\displaystyle A = 2P) in 10\displaystyle 10 years under Compound Interest. (1+r)10=2(1 + r)^{10} = 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)10\displaystyle 2 = (1 + r)^{10}** (1+r)t=[(1+r)10]3(1 + r)^t = \left[(1 + r)^{10}\right]^3 (1+r)t=(1+r)30    t=30 years(1 + r)^t = (1 + r)^{30} \implies t = 30 \text{ years} Hence, **Option B** 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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