Question 2 You deposit \( \$ 5000 \) each year into an account earning 6\% interest compounded annually. How much will you have in the account in 25 years? Note: Round your answer to the nearest cent. Question Help: Video 1 Video 2 Message instructor Calculator

We are dealing with an annuity where you deposit a fixed amount each year. The formula for the future value of an annuity (with deposits made at the end of each period) is given by \[ \text{FV} = D \times \frac{(1+r)^n - 1}{r} \] where - \( D \) is the annual deposit, - \( r \) is the annual interest rate (in decimal), and - \( n \) is the number of years. Given in the problem: - \( D = 5000 \), - \( r = 0.06 \), and - \( n = 25 \). Substitute these values into the formula: \[ \text{FV} = 5000 \times \frac{(1.06)^{25} - 1}{0.06} \] Step 1: Compute \((1.06)^{25}\). Using a calculator, \[ (1.06)^{25} \approx 4.29187 \] Step 2: Subtract 1: \[ 4.29187 - 1 = 3.29187 \] Step 3: Divide by \(0.06\): \[ \frac{3.29187}{0.06} \approx 54.8645 \] Step 4: Multiply by 5000: \[ \text{FV} \approx 5000 \times 54.8645 \approx 274322.50 \] Thus, after 25 years, the amount in the account will be approximately \[ \boxed{\$274322.50} \]