Simple interest is an important framework to start learning about the Time value of Money.
If you are going to receive [tex]$2,000 in six years from now, how much is that worth today, assuming 5% annual
simple interest?
$[/tex]1,780.32
[tex]$2,600.00
$[/tex]1,904.76
$1,538.46



Answer :

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