Final answer:
To calculate the future value of a coin after 5 years at 9% annual growth, use the compound interest formula, resulting in a value of approximately $1.80.
Step-by-step explanation:
The question asks to calculate the future value of a coin after 5 years, given an initial value and an annual growth rate. This is a compound interest problem. The formula to calculate future value with compound interest is Future Value = Present Value * (1 + rate)^number of years. In this case, the Present Value is $1.17, the rate is 9% or 0.09, and the time is 5 years.
So, the calculation would be: $1.17 * (1 + 0.09)^5.
Executing this calculation, the future value of the coin after 5 years would be:
Future Value = $1.17 * (1.09)^5 = $1.17 * 1.53862 = $1.80 (approximately).