\( \$ 3,100 \) is invested in an account with a \( 3.2 \% \) interest rate that is compounded quarterly. How much money is in the account at the end of one year? \[ \$[?] \]

To find the amount in the account at the end of one year when the interest is compounded quarterly, 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 amount of money). - \(r\) is the annual interest rate (in decimal). - \(n\) is the number of times that interest is compounded per year. - \(t\) is the number of years the money is invested. Given: - \(P = 3100\) - \(r = 0.032\) (which is \(3.2\%\)) - \(n = 4\) (quarterly compounding) - \(t = 1\) Now, plug in the values: \[ A = 3100 \left(1 + \frac{0.032}{4}\right)^{4 \times 1} \] \[ A = 3100 \left(1 + 0.008\right)^{4} \] \[ A = 3100 \left(1.008\right)^{4} \] \[ A \approx 3100 \times 1.0324 \approx 3200.44 \] So, the amount in the account at the end of one year is approximately \( \$3200.44 \).