You deposit \( \$ 2000 \) in an account earning \( 5 \% \) interest compounded quarterly. How much will you have in the account in 15 years? Round value to the nearest cent.

To calculate the future value of the deposit, you can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit or investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested or borrowed. In this case, you have: - \( P = 2000 \) - \( r = 0.05 \) - \( n = 4 \) (quarterly compounding) - \( t = 15 \) Plugging in these values: \[ A = 2000 \left(1 + \frac{0.05}{4}\right)^{4 \times 15} \] \[ A = 2000 \left(1 + 0.0125\right)^{60} \] \[ A = 2000 \left(1.0125\right)^{60} \] \[ A \approx 2000 \times 2.012196 \] \[ A \approx 4024.39 \] So, you will have approximately **\$4024.39** in the account after 15 years.