Tamara invested \( \$ 15,000 \) in a money market account with an interest rate of \( 2.25 \% \) compounded semiannually. Five years later, Tamara withdrew the full amount to put toward the down payment on a new house. How much did Tamara withdraw from the account? Tamara withdrew \( \$ \square \) (Round to the nearest cent as needed.)

To calculate the amount Tamara withdrew after 5 years from a money market account with a principal of \( \$ 15,000 \), an interest rate of \( 2.25\% \) compounded semiannually, we can use the compound interest formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after \( n \) years, including interest. - \( P \) is the principal amount (the initial 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. Plugging in the values: - \( P = 15000 \) - \( r = 0.0225 \) (2.25% as a decimal) - \( n = 2 \) (since it’s compounded semiannually) - \( t = 5 \) Now we can substitute these values into the formula: \[ A = 15000 \left(1 + \frac{0.0225}{2}\right)^{2 \times 5} \] \[ A = 15000 \left(1 + 0.01125\right)^{10} \] \[ A = 15000 \left(1.01125\right)^{10} \] Calculating \( (1.01125)^{10} \): \[ (1.01125)^{10} \approx 1.117202 \] Now plug this back into the formula: \[ A \approx 15000 \times 1.117202 \approx 16758.03 \] Thus, Tamara withdrew approximately \( \$ 16,758.03 \) from the account. Tamara withdrew \( \$ 16,758.03 \).