Question

A person invested Rs.15,000 in a mutual fund; it became Rs.25,000. If CAGR is 8.88%, then the number of years \( n \) is: [Use \( -\log 1.667 = 0.2219 \); \( \log 1.089 = 0.0370 \)]

• A. 2
• B. 4
• C. 7
• D. 6

Hint:

CAGR smoothens out volatility over a period, providing a single annual growth rate.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Compound Annual Growth Rate (CAGR) formula is: \( \text{Ending Value} = \text{Beginning Value} \times (1 + \text{CAGR})^n \), where \( n \) is the number of years.

Step 2: Detailed Explanation:
Given:
Beginning Value = ₹15,000
Ending Value = ₹25,000
CAGR = 8.88% = 0.0888
\( 25,000 = 15,000 \times (1 + 0.0888)^n \)
\( \frac{25,000}{15,000} = (1.0888)^n \)
\( 1.667 = (1.0888)^n \)
Taking the logarithm on both sides:
\( \log(1.667) = n \log(1.0888) \)
Using the provided values (approximating 1.0888 to 1.089):
\( 0.2219 = n \times 0.0370 \)
\( n = \frac{0.2219}{0.0370} \approx 5.997 \approx 6 \).

Step 3: Final Answer:
The investment period is 6 years.