Final answer:
The rate of return on the sale of the coin that was purchased for $1 and is now worth $450 after 50 years is approximately 13%. This is determined using the formula for the annual compound interest rate.
Step-by-step explanation:
To calculate the rate of return on the gold coin that Julian's great-grandfather purchased for $1 and is now worth $450 after 50 years, we can use the formula for the annual compound interest rate, which is:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In Julian's case, we don't have the number of times that interest is compounded annually, but since it is a single investment over time, we can consider the interest as compounded once per year.
Therefore, we can simplify the formula to just A = P(1 + r)^t, and we need to solve for r, knowing that A = $450, P = $1, and t = 50 years.
After solving the equation for r, we can approximate the rate of return. In this situation, the answer is approximately 13%, which corresponds to option A.