Mathematics of FinancePYQ Sept 25Question 4118 of 507
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Ms. Y invested ₹ 2,00,000 in a mutual fund equity scheme. She redeemed entire investment after 96 months and received ₹ 6,00,000 after redemption. What was the Compound Annual Growth Rate (CAGR) in percentage? (Given: 1.14724=1.732\displaystyle 1.1472^4 = 1.732)

Options

A14.72
B15.72
C13.72
D12.72
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Correct Answer

✅ Option a — 14.72

All Options:

  • A14.72
  • B15.72
  • C13.72
  • D12.72

Detailed Solution & Explanation

Given: Initial investment (PV\displaystyle PV) = ₹ 2,00,000 Amount received after redemption (FV\displaystyle FV) = ₹ 6,00,000 Time period = 96 months = 9612=8\displaystyle \frac{96}{12} = 8 years
The Compound Annual Growth Rate (CAGR) is given by: CAGR=(FVPV)1/n−1CAGR = \left(\frac{FV}{PV}\right)^{1/n} - 1 where n=8\displaystyle n = 8 years.
Substitute the values: CAGR=(6,00,0002,00,000)1/8−1CAGR = \left(\frac{6,00,000}{2,00,000}\right)^{1/8} - 1 CAGR=31/8−1CAGR = 3^{1/8} - 1
We are given the hint: 1.14724=1.732\displaystyle 1.1472^4 = 1.732. Note that 1.732≈3=31/2\displaystyle 1.732 \approx \sqrt{3} = 3^{1/2}. So: (1.1472)4≈31/2(1.1472)^4 \approx 3^{1/2} Squaring both sides: ((1.1472)4)2≈3  ⟹  1.14728≈3\left((1.1472)^4\right)^2 \approx 3 \implies 1.1472^8 \approx 3 Thus: 31/8≈1.14723^{1/8} \approx 1.1472 Substitute this back: CAGR≈1.1472−1=0.1472=14.72%CAGR \approx 1.1472 - 1 = 0.1472 = 14.72\%
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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