Question 11
50 years ago your parents purchased a non-dividend paying share in Pinder Ltd for 0.21. today that  12.60. Which of the following is closest to the average annual geometric rate of return
that your parents have earned on the share?
(a) 5.20%
(b) 5.73%
(c) 8.53%
(d) 9.08%


To calculate the average annual geometric rate of return, we use the geometric mean formula for returns, which is:

\[
r = \left( \frac{P_{\text{end}}}{P_{\text{start}}} \right)^{\frac{1}{t}} - 1
\]

Where:
- \(P_{\text{end}} = 12.60\) (the price of the share today),
- \(P_{\text{start}} = 0.21\) (the price of the share 50 years ago),
- \(t = 50\) years (the time span).

Let's calculate it.

\[
r = \left( \frac{12.60}{0.21} \right)^{\frac{1}{50}} - 1
\]

Now, let me calculate that.The average annual geometric rate of return is approximately **8.53%**, which matches option **(c) 8.53%**.

Would you like further details or have any questions about the calculation?

Here are 5 related questions for further exploration:
1. How does the geometric mean differ from the arithmetic mean when calculating returns?
2. What impact does compounding have on the geometric rate of return?
3. What would happen if dividends were included in the return calculation?
4. How would a shorter time period (e.g., 20 years) affect the geometric rate of return?
5. What are other methods for evaluating long-term investment returns?

**Tip:** The geometric rate of return is more accurate for assessing long-term investments because it accounts for compounding over time.

50 years ago your parents purchased a non-dividend paying share in Pinder Ltd for 0.21. Today that share is worth 12.60. Which of the following is closest to the average annual geometric rate of return that your parents have earned on the share? (a) 5.20% (b) 5.73% (c) 8.53% (d) 9.08%

Learn how to calculate the average annual geometric rate of return for a non-dividend paying share purchased 50 years ago at 0.21 and now worth 12.60. This detailed solution includes key financial concepts like geometric returns, compounding, and exponential growth. Suitable for finance students and advanced high school math learners.

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