Mathematics of FinanceMCQMTP Mar 22Question 1352 of 512
All Questions

In how many years will a sum of money become double at 5%\displaystyle 5\% p.a compound interest

Options

A14\displaystyle 14 years
B15\displaystyle 15 years
C16\displaystyle 16 years
D14.3\displaystyle 14.3 years
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Correct Answer

✅ Option d — 14.3\displaystyle 14.3 years

All Options:

  • A14\displaystyle 14 years
  • B15\displaystyle 15 years
  • C16\displaystyle 16 years
  • D14.3\displaystyle 14.3 years

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Detailed Solution & Explanation

**Derivation of Doubling Time under Compound Interest** Given: - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum compounded annually - Let the sum be P\displaystyle P. Amount (A\displaystyle A) = 2P\displaystyle 2P **Step 1: Set up the compound interest equation** A=P(1+r)tA = P(1 + r)^t 2P=P(1.05)t2P = P(1.05)^t 2=(1.05)t2 = (1.05)^t **Step 2: Solve for t\displaystyle t using logarithms** ln⁡(2)=tln⁡(1.05)\ln(2) = t \ln(1.05) t=ln⁡(2)ln⁡(1.05)t = \frac{\ln(2)}{\ln(1.05)} Using log values: ln⁡(2)≈0.693147\ln(2) \approx 0.693147 ln⁡(1.05)≈0.048790\ln(1.05) \approx 0.048790 t=0.6931470.048790≈14.21 years≈14.3 yearst = \frac{0.693147}{0.048790} \approx 14.21 \text{ years} \approx 14.3 \text{ years} *(Note: The database lists Option C (16\displaystyle 16 years) as correct, which is a textbook discrepancy. The mathematically closest option is Option D.)* Hence, **Option D** 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

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.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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