Question

Compute the requested value(s) for each scenario. Show all component numbers that factor into determination of the final answer(s) a. On January 1, 1963, a kid from Sioux Falls purchased a limited edition Superman comic at the original market price of 12 cents. On January 1, 1997 (34 years later), the comic was sold at auction for $2,500. What annual rate of return did this kid earn on the comic?

Answer 1

The annual rate of return on the limited edition Superman comic, purchased for 12 cents on January 1, 1963, and sold at auction for $2,500 on January 1, 1997, is approximately 15.45%.

Step-by-step explanation:

To determine the annual rate of return (ARR), we use the compound annual growth rate (CAGR) formula:

`\[ CAGR = \left( \frac{{\text{{Ending Value}}}}{{\text{{Beginning Value}}}} \right)^{\frac{1}{\text{{Number of Years}}}} - 1 \]`

In this case, the beginning value is the original market price of the comic in 1963 (12 cents), the ending value is the auction price in 1997 ($2,500), and the number of years is 34.

`\[ CAGR = \left( \frac{{2,500}}{{0.12}} \right)^{(1)/(34)} - 1 \]`

After calculating, the CAGR is approximately 0.1545 or 15.45%. This indicates that the kid from Sioux Falls earned an annual return of 15.45% on the limited edition Superman comic over the 34-year period.