Interest and TVM You deposit \( \$ 1000 \) in an account that pays \( 7 \% \) interest compounded semiannually. After 2 years, the interest rate is increased to \( 7.44 \% \) compounded quarterly. What will be the value of the account after a total of 4 years? Click the icon to view some finance formulas. The value of the acoount will be \( \$ \square \). (Round to the nearest dollar as needed.)

To find the value of the account after 4 years, we first calculate the amount after the initial 2 years at the 7% interest rate compounded semiannually. The formula to use is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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 (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. For the first 2 years: - \(P = 1000\) - \(r = 0.07\) - \(n = 2\) - \(t = 2\) Using the formula: \[ A = 1000 \left(1 + \frac{0.07}{2}\right)^{2 \times 2} = 1000 \left(1 + 0.035\right)^{4} = 1000 \left(1.035\right)^{4} \approx 1000 \times 1.148882 \approx 1148.88 \] So, after 2 years, the account balance is approximately \$1149. Now, we proceed to the next 2 years with the increased interest rate of 7.44% compounded quarterly. Again, using the same formula with: - \(P \approx 1149\) - \(r = 0.0744\) - \(n = 4\) - \(t = 2\) Calculating this part: \[ A = 1149 \left(1 + \frac{0.0744}{4}\right)^{4 \times 2} = 1149 \left(1 + 0.0186\right)^{8} \approx 1149 \left(1.0186\right)^{8} \approx 1149 \times 1.158496 \approx 1338.88 \] Rounding to the nearest dollar, the value of the account after a total of 4 years will be approximately **\$1339**.