Mathematics of FinancePYQ Jan 26Question 4506 of 507
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If an amount is compounded annually so that it tripled itself in 4 years, then the annual rate of interest is (Given that 31/4=1.316\displaystyle 3^{1/4} = 1.316)

Options

A13.6%
B31.1%
C31.6%
D11.3%
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Correct Answer

Option c31.6%

All Options:

  • A13.6%
  • B31.1%
  • C31.6%
  • D11.3%

Detailed Solution & Explanation

Let the principal amount be P\displaystyle P and the annual rate of interest be r\displaystyle r.

The compound interest formula for annual compounding is:
A=P(1+r)tA = P(1 + r)^t
where:
- A\displaystyle A is the final amount after time t\displaystyle t.
- P\displaystyle P is the initial principal amount.
- r\displaystyle r is the annual rate of interest (as a decimal).
- t\displaystyle t is the time in years.

Given that the amount triples itself in 4\displaystyle 4 years (t=4\displaystyle t = 4, A=3P\displaystyle A = 3P):
3P=P(1+r)43P = P(1 + r)^4
3=(1+r)43 = (1 + r)^4
Taking the fourth root on both sides:
1+r=31/41 + r = 3^{1/4}

Using the given approximation 31/4=1.316\displaystyle 3^{1/4} = 1.316:
1+r=1.3161 + r = 1.316
r=1.3161r = 1.316 - 1
r=0.316r = 0.316
Converting to a percentage:
r=0.316×100%=31.6% per annumr = 0.316 \times 100\% = 31.6\% \text{ per annum}

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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