You deposit \( \$ 1000 \) in an account that pays \( 7 \% \) interest compounded semiannually. After 2 years, the interest rate is increased to \( 7.32 \% \) compounded quarterly. What will be the value of the account after a total of 4 years? i) Click the icon to view some finance formulas. The value of the account will be \( \$ \square \). (Round to the nearest dollar as needed.)

To solve for the value of the account after 4 years, let's break it down: 1. For the first 2 years at 7% interest compounded semiannually: - The formula for compound interest is \( A = P(1 + \frac{r}{n})^{nt} \) where: - \( P = 1000 \) (initial deposit), - \( r = 0.07 \) (annual interest rate), - \( n = 2 \) (number of times interest is compounded per year), - \( t = 2 \) (years). - Calculating: \( A = 1000(1 + \frac{0.07}{2})^{2 \times 2} = 1000(1 + 0.035)^{4} = 1000(1.035)^{4} \approx 1000 \times 1.148882 \approx 1148.88 \). 2. For the next 2 years at 7.32% compounded quarterly: - Using the same formula with \( P \) now being the new amount (\$1148.88), \( r = 0.0732 \), \( n = 4 \), and \( t = 2 \): - Calculating: \( A = 1148.88(1 + \frac{0.0732}{4})^{4 \times 2} = 1148.88(1 + 0.0183)^{8} = 1148.88(1.0183)^{8} \approx 1148.88 \times 1.151331 \approx 1320.03 \). Rounding to the nearest dollar, the value of the account after a total of 4 years will be \( \$1320 \).