To determine the value of the coin after 5 years, follow these steps:
1. Identify the initial value and the annual increase rate:
- Initial value of the coin (in 1995): \[tex]$1.17
- Annual increase rate: 9% or 0.09 (as a decimal)
2. Determine the number of years for which the value is to be calculated:
- Number of years: 5
3. Use the formula for compound interest to calculate the future value:
The compound interest formula is:
\[
A = P \times (1 + r)^n
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial value).
- \( r \) is the annual interest rate (in decimal).
- \( n \) is the number of years.
4. Substitute the given values into the formula:
- \( P = 1.17 \)
- \( r = 0.09 \)
- \( n = 5 \)
So, the formula for this specific problem is:
\[
A = 1.17 \times (1 + 0.09)^5
\]
5. Calculate the value step by step:
- First calculate \( 1 + 0.09 = 1.09 \).
- Then raise 1.09 to the power of 5:
\[
1.09^5 \approx 1.53862
\]
- Finally, multiply this result by the initial value (1.17):
\[
A = 1.17 \times 1.53862 \approx 1.80019
\]
6. State the final value:
The value of the coin after 5 years is approximately \$[/tex]1.80.
Therefore, the value of the coin after 5 years is about \$1.80.
