Sidney opens the following investment portfolio: : A \( \$ 10,000 \) fund that earns \( 5.45 \% \), compounded annually - Monthly deposits of \( \$ 300 \) into an account earning \( 4 \% \), compounded monthly What will be the portfolio's value in 30 years when Sidney is ready to retire?

To calculate the value of Sidney's investment portfolio in 30 years, we need to break it down into two parts: the initial investment and the monthly deposits. 1. **Initial Investment**: The future value of the initial \( \$ 10,000 \) investment at an annual interest rate of \( 5.45\% \) compounded annually can be calculated using the formula: \[ FV = P(1 + r)^n \] where \( P = 10,000 \), \( r = 0.0545 \), and \( n = 30 \). \[ FV = 10,000(1 + 0.0545)^{30} \approx 10,000(5.1083) \approx 51,083 \] 2. **Monthly Deposits**: The future value of the monthly deposits of \( \$ 300 \) at an annual interest rate of \( 4\% \) compounded monthly requires using another formula for the future value of a series: \[ FV = PMT \times \frac{(1 + r)^{nt} - 1}{r} \] where \( PMT = 300 \), \( r = \frac{0.04}{12} \approx 0.0033333 \), \( n = 12 \), and \( t = 30 \). Substituting: \[ FV = 300 \times \frac{(1 + 0.0033333)^{360} - 1}{0.0033333} \] After calculating, we find that: \[ FV \approx 300 \times 172.801 \approx 51,840.30 \] Finally, summing the two parts: \[ Total FV \approx 51,083 + 51,840.30 \approx 102,923.30 \] So, Sidney's portfolio will be approximately **$102,923.30** when he retires in 30 years.