Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 3955 of 512
All Questions

How long will it take for a principal to double if money is worth 12%\displaystyle 12\% compounded monthly?

Options

A4.25\displaystyle 4.25 years
B5.81\displaystyle 5.81 years
C6.93\displaystyle 6.93 years
DNone of these
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Correct Answer

✅ Option b — 5.81\displaystyle 5.81 years

All Options:

  • A4.25\displaystyle 4.25 years
  • B5.81\displaystyle 5.81 years
  • C6.93\displaystyle 6.93 years
  • DNone of these

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Detailed Solution & Explanation

Let the principal be P\displaystyle P. Given parameters: * Nominal rate of interest (r\displaystyle r) = 12%\displaystyle 12\% p.a. =0.12\displaystyle = 0.12 * Compounding frequency (m\displaystyle m) = 12\displaystyle 12 (compounded monthly) * Monthly rate (i\displaystyle i) = 0.1212=0.01\displaystyle \frac{0.12}{12} = 0.01 We want to find the number of years (t\displaystyle t) for the principal to double: A=P(1+i)12tA = P(1+i)^{12t} 2P=P(1.01)12t2P = P(1.01)^{12t} (1.01)12t=2(1.01)^{12t} = 2 Taking natural logarithms on both sides: 12tln⁡(1.01)=ln⁡(2)12t \ln(1.01) = \ln(2) 12t≈0.6931470.009950≈69.66 months12t \approx \frac{0.693147}{0.009950} \approx 69.66 \text{ months} Solving for t\displaystyle t: t≈69.6612≈5.81 yearst \approx \frac{69.66}{12} \approx 5.81 \text{ years} Thus, it will take approximately 5.81\displaystyle 5.81 years to double. 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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