10 Points] DETAILS MY NOTES AUFQR2 4.1.014. Find the future value (in dollars) of a 2 -year investment of \( \$ 6,725 \) into a simple interest rate account that has an annual simple interest rate of \( 3.5 \% \). \( \$ \square \)

To find the future value of an investment in a simple interest account, we can use the formula for simple interest: \[ FV = P + I \] where: - \( FV \) is the future value, - \( P \) is the principal amount (initial investment), - \( I \) is the interest earned. The interest \( I \) can be calculated using the formula: \[ I = P \times r \times t \] where: - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years. ### Step 1: Identify the known values - \( P = 6725 \) - \( r = 3.5\% = 0.035 \) - \( t = 2 \) ### Step 2: Calculate the interest earned Now, we can calculate the interest \( I \): \[ I = 6725 \times 0.035 \times 2 \] ### Step 3: Calculate the future value After calculating \( I \), we can find the future value \( FV \): \[ FV = P + I \] Let's perform the calculations. First, calculate \( I \): \[ I = 6725 \times 0.035 \times 2 \] Now, I will calculate this value. Calculate the value by following steps: - step0: Calculate: \(6725\times 0.035\times 2\) - step1: Multiply the terms: \(235.375\times 2\) - step2: Multiply the numbers: \(470.75\) The interest earned \( I \) is calculated as: \[ I = 6725 \times 0.035 \times 2 = 470.75 \] ### Step 4: Calculate the future value Now, we can find the future value \( FV \): \[ FV = P + I = 6725 + 470.75 \] Let's calculate this final value. Calculate the value by following steps: - step0: Calculate: \(6725+470.75\) - step1: Add the numbers: \(7195.75\) The future value \( FV \) is calculated as: \[ FV = 6725 + 470.75 = 7195.75 \] Thus, the future value of the 2-year investment of \( \$ 6,725 \) at an annual simple interest rate of \( 3.5\% \) is: \[ \boxed{7195.75} \]