To solve this problem, we need to calculate the simple interest earned and the future value of the investment after 2 years.
Simple interest can be calculated using the formula:
[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Where:
- The principal (initial investment) is [tex]$10,000
- The annual interest rate is 5%, which can be expressed as 0.05 in decimal form
- The time period is 2 years
Let's plug these values into the formula:
\[ \text{Simple Interest} = 10,000 \times 0.05 \times 2 \]
Multiplying these values, we get:
\[ \text{Simple Interest} = 10,000 \times 0.05 \times 2 = 1,000 \]
a) Therefore, the interest earned over 2 years is $[/tex]1,000 (rounded to the nearest cent).
Next, we need to calculate the future value of the investment. The future value is the sum of the principal and the interest earned. The formula for the future value is:
[tex]\[ \text{Future Value} = \text{Principal} + \text{Simple Interest} \][/tex]
Substituting the known values:
[tex]\[ \text{Future Value} = 10,000 + 1,000 \][/tex]
Adding these together, we get:
[tex]\[ \text{Future Value} = 11,000 \][/tex]
b) Therefore, the future value of the investment is [tex]$11,000 (rounded to the nearest cent).
To summarize:
a) You will earn $[/tex]1,000 in interest.
b) The future value is $11,000.
