a. If upon retirement in 20 years Simon plans to invest $400,000 in a fund that earns 5%, what is the maximum annual withdrawal he can make over the following 15 years?
To find the maximum annual withdrawal Simon can make over the following 15 years, we need to calculate the compound interest earned on his investment and then determine the annual withdrawal amount.
Step 1: Calculate the future value of the investment after 20 years.
We'll use the compound interest formula: FV = PV * (1 + r)^n, where FV is the future value, PV is the present value (initial investment), r is the interest rate, and n is the number of years.
PV = $400,000 (the initial investment)
r = 5% (convert to decimal: 0.05)
n = 20 (number of years)
FV = $400,000 * (1 + 0.05)^20
FV = $400,000 * (1.05)^20
FV ≈ $904,556.78
Step 2: Determine the maximum annual withdrawal amount.
We'll divide the future value by the number of years Simon plans to withdraw the money (15) to find the annual withdrawal amount.
Annual Withdrawal Amount = FV / n
= $904,556.78 / 15
≈ $60,303.78
Therefore, Simon can withdraw a maximum of approximately $60,303.78 annually over the following 15 years if he invests $400,000 in a fund earning 5%.