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 CAGR formula is \( Final Value = Initial Value \times (1 + CAGR)^n \).

Step 2: Key Formula or Approach:
\( 25,000 = 15,000 \times (1 + 0.0888)^n \)
\( 25/15 = (1.0888)^n \implies 1.667 = (1.0888)^n \).

Step 3: Detailed Explanation:
Taking log on both sides:
\( \log(1.667) = n \times \log(1.0888) \).
Given \( \log(1.089) \approx 0.0370 \).
\( n = \log(1.667) / \log(1.0888) \).
\( n \approx 0.2219 / 0.0370 \approx 5.997 \).
Rounding to the nearest integer gives 6.

Step 4: Final Answer:
The number of years is 6.