Mathematics of FinanceMCQMTP Apr 21Question 1329 of 512
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A sum amount to Rs. 1331\displaystyle 1331 at a principal of Rs.1000\displaystyle 1000 at 10%\displaystyle 10\% CI. Find the time

Options

A3.31\displaystyle 3.31 years
B4\displaystyle 4 years
C3\displaystyle 3 years
D2\displaystyle 2 years
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Correct Answer

✅ Option c — 3\displaystyle 3 years

All Options:

  • A3.31\displaystyle 3.31 years
  • B4\displaystyle 4 years
  • C3\displaystyle 3 years
  • D2\displaystyle 2 years

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Detailed Solution & Explanation

**Derivation of Time Period** Given: - Principal (P\displaystyle P) = Rs. 1,000\displaystyle \text{Rs. }1,000 - Amount (A\displaystyle A) = Rs. 1,331\displaystyle \text{Rs. }1,331 - Rate of Interest (r\displaystyle r) = 10%\displaystyle 10\% per annum compounded annually **Step 1: Set up the Compound Interest equation** A=P(1+r)tA = P(1 + r)^t 1331=1000(1+0.10)t1331 = 1000(1 + 0.10)^t 1.331=(1.10)t1.331 = (1.10)^t **Step 2: Solve for t\displaystyle t** Since (1.10)3=1.331\displaystyle (1.10)^3 = 1.331, we have: (1.10)3=(1.10)t  ⟹  t=3 years(1.10)^3 = (1.10)^t \implies t = 3 \text{ years} 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

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