To determine which items you can buy in two years if you invest \[tex]$1,500 at an annual interest rate of 5%, we need to calculate the future value of this investment using the compound interest formula:
\[ \text{Future Value} = P \times (1 + i)^t \]
Where:
- \( P \) is the initial principal (the amount of money you start with),
- \( i \) is the annual interest rate,
- \( t \) is the number of years the money is invested.
Given:
- \( P = 1500 \) dollars,
- \( i = 0.05 \) (5 percent as a decimal),
- \( t = 2 \) years.
Plugging in the values:
\[ \text{Future Value} = 1500 \times (1 + 0.05)^2 \]
\[ \text{Future Value} = 1500 \times 1.05^2 \]
\[ \text{Future Value} = 1500 \times 1.1025 \]
\[ \text{Future Value} = 1653.75 \]
So, after 2 years, the investment will be worth \$[/tex]1653.75.
Next, we will compare this future value with the prices of the items:
- Electronics: \[tex]$1650
- Fitness equipment: \$[/tex]1700
- Holiday package: \[tex]$2000
Now we check which items can be purchased with \$[/tex]1653.75:
- The price of the electronics (\[tex]$1650) is less than or equal to \$[/tex]1653.75, so you can buy the electronics.
- The price of the fitness equipment (\[tex]$1700) is greater than \$[/tex]1653.75, so you cannot buy the fitness equipment.
- The price of the holiday package (\[tex]$2000) is greater than \$[/tex]1653.75, so you cannot buy the holiday package.
Therefore, the correct answer is:
A. Electronics worth \$1650
