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 determine the future value of your account after a total of 4 years with the given interest rates and compounding periods, we'll break the calculation into two parts: 1. **First 2 Years:** - **Principal (\( P \))**: \$1,000 - **Annual Interest Rate (\( r \))**: 7% or 0.07 - **Compounding Frequency (\( n \))**: Semiannually (\( n = 2 \)) - **Time (\( t \))**: 2 years The formula for compound interest is: \[ \text{Future Value} = P \left(1 + \frac{r}{n}\right)^{nt} \] Plugging in the values: \[ \text{Future Value after 2 years} = 1000 \times \left(1 + \frac{0.07}{2}\right)^{2 \times 2} = 1000 \times (1.035)^4 \approx 1000 \times 1.1475 = \$1,147.50 \] 2. **Next 2 Years:** - **New Principal (\( P \))**: \$1,147.50 (from the first 2 years) - **New Annual Interest Rate (\( r \))**: 7.32% or 0.0732 - **Compounding Frequency (\( n \))**: Quarterly (\( n = 4 \)) - **Time (\( t \))**: 2 years Using the compound interest formula again: \[ \text{Future Value after 4 years} = 1147.50 \times \left(1 + \frac{0.0732}{4}\right)^{4 \times 2} = 1147.50 \times (1.0183)^8 \approx 1147.50 \times 1.1562 = \$1,327 \] **Final Answer:** The value of the account after 4 years will be **\$1,327**.