To determine the present value of [tex]$2,000 to be received in six years, assuming an annual simple interest rate of 5%, we can use the formula for calculating present value in the context of simple interest. The formula is:
\[ \text{Present Value} = \frac{\text{Future Value}}{1 + (\text{interest rate} \times \text{time period})} \]
Let's break it down step by step:
1. Identify the future value (FV):
\[ \text{Future Value} = 2000 \]
2. Identify the annual interest rate (r):
\[ \text{Interest Rate} = 0.05 \]
3. Identify the time period in years (t):
\[ \text{Time Period} = 6 \]
4. Plug these values into the present value formula:
\[ \text{Present Value} = \frac{2000}{1 + (0.05 \times 6)} \]
5. Simplify the expression inside the parentheses:
\[ 1 + (0.05 \times 6) = 1 + 0.30 = 1.30 \]
6. Perform the division:
\[ \text{Present Value} = \frac{2000}{1.30} \]
7. Calculate the present value:
\[ \text{Present Value} = 1538.4615384615383 \]
Rounding to two decimal places (if required):
\[ \text{Present Value} \approx 1538.46 \]
Therefore, the amount you would need to invest today to receive $[/tex]2,000 in six years at a 5% annual simple interest rate is approximately [tex]$1,538.46.
Hence, the correct answer is the last option:
$[/tex]1,538.46
