Mathematics of FinanceMCQPYQ May 20Question 1302 of 512
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The time by which a sum of money would treble itself at 8%\displaystyle 8\% p.a. C. I. is

Options

A14.28\displaystyle 14.28 years
B14\displaystyle 14 years
C12\displaystyle 12 years
Dnone of these
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Correct Answer

Option a14.28\displaystyle 14.28 years

All Options:

  • A14.28\displaystyle 14.28 years
  • B14\displaystyle 14 years
  • C12\displaystyle 12 years
  • Dnone of these

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Detailed Solution & Explanation

**Derivation of Trebling Time under Compound Interest** Given: - Rate of Interest (r\displaystyle r) = 8%\displaystyle 8\% per annum compounded annually - Let the principal be P\displaystyle P. We want the amount to treble (A=3P\displaystyle A = 3P). **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 3P=P(1+0.08)t3P = P(1 + 0.08)^t 3=(1.08)t3 = (1.08)^t **Step 2: Solve for t\displaystyle t using logarithms** ln(3)=tln(1.08)\ln(3) = t \ln(1.08) t=ln(3)ln(1.08)t = \frac{\ln(3)}{\ln(1.08)} Using log values: ln(3)1.098612\ln(3) \approx 1.098612 ln(1.08)0.076961\ln(1.08) \approx 0.076961 t=1.0986120.07696114.28 yearst = \frac{1.098612}{0.076961} \approx 14.28 \text{ years} Hence, **Option A** 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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