Mathematics of FinancePYQ May 25Question 4019 of 507
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Madhu invests ₹ 15,000 in a scheme and at the time of maturity the amount became ₹ 25,000. If CAGR for this investment is 8.88%, calculate the approximate number of years for which she has invested the amount.[Given that log(1.667)=0.2219\displaystyle \log(1.667) = 0.2219 and log(1.089)=0.037\displaystyle \log(1.089) = 0.037]

Options

A6 years
B7.7 years
C5.5 years
D7 years
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Correct Answer

Option a6 years

All Options:

  • A6 years
  • B7.7 years
  • C5.5 years
  • D7 years

Detailed Solution & Explanation

The formula for compound interest / CAGR is:
A=P(1+g)nA = P(1 + g)^n
Where:
- A=25,000\displaystyle A = ₹ 25,000 (Maturity amount)
- P=15,000\displaystyle P = ₹ 15,000 (Initial investment amount)
- g=8.88%=0.0888\displaystyle g = 8.88\% = 0.0888 (CAGR rate)
- n\displaystyle n = Number of years of investment

Substituting the values into the formula:
25000=15000×(1+0.0888)n25000 = 15000 \times (1 + 0.0888)^n
Divide both sides by 15000\displaystyle 15000:
2500015000=(1.0888)n\frac{25000}{15000} = (1.0888)^n
1.667(1.0888)n1.667 \approx (1.0888)^n
Take the logarithm on both sides:
log(1.667)=log((1.0888)n)\log(1.667) = \log\left((1.0888)^n\right)
Using properties of logarithms:
log(1.667)=nlog(1.0888)\log(1.667) = n \log(1.0888)

We are given the values:
log(1.667)=0.2219\log(1.667) = 0.2219
log(1.089)=0.037\log(1.089) = 0.037
Note that the base 1.08881.089\displaystyle 1.0888 \approx 1.089. Therefore, we can approximate log(1.0888)log(1.089)=0.037\displaystyle \log(1.0888) \approx \log(1.089) = 0.037.
Substitute these log values into the equation:
0.2219n×0.0370.2219 \approx n \times 0.037
n0.22190.0375.9976 yearsn \approx \frac{0.2219}{0.037} \approx 5.997 \approx 6 \text{ years}
Thus, the approximate duration of the investment is 6\displaystyle 6 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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