To solve this problem, we need to calculate the future value of the investment after two years and then compare it to the costs of the items given.
### Step-by-Step Solution:
1. Determine the initial investment, interest rate, and time period:
- Initial investment ([tex]\(P\)[/tex]): \[tex]$1,500
- Annual interest rate (\(i\)): 5% or 0.05
- Time period (\(t\)): 2 years
2. Calculate the future value (\(FV\)) using the formula:
\[
\text{FV} = P \times (1 + i)^t
\]
- Substituting the values:
\[
\text{FV} = 1500 \times (1 + 0.05)^2
\]
3. Future value calculation:
- First calculate the amount inside the parentheses:
\[
1 + 0.05 = 1.05
\]
- Then, raise this to the power of 2:
\[
1.05^2 = 1.1025
\]
- Finally, multiply by the initial investment:
\[
\text{FV} = 1500 \times 1.1025 = 1653.75
\]
- So, the future value after 2 years is \$[/tex]1,653.75.
4. Determine which items can be bought:
- Item A (electronics worth \[tex]$1,650): Yes, because \$[/tex]1,653.75 ≥ \[tex]$1,650.
- Item B (fitness equipment worth \$[/tex]1,700): No, because \[tex]$1,653.75 < \$[/tex]1,700.
- Item C (holiday package worth \[tex]$2,000): No, because \$[/tex]1,653.75 < \[tex]$2,000.
### Conclusion:
- You can buy electronics worth \$[/tex]1,650.
- You cannot buy fitness equipment worth \[tex]$1,700.
- You cannot buy a holiday package worth \$[/tex]2,000.
So, the correct answer is:
A. Electronics worth \$1,650
