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 that Simon can make over the following 15 years, we need to calculate the future value of his investment after 20 years. This will give us the amount he will have available for withdrawal.
Let's use the formula for future value (FV) of an investment:
FV = PV * (1 + r)^n
Where:
PV = Present value (initial investment) = $400,000
r = Interest rate per period = 5% (expressed as a decimal, so 0.05)
n = Number of periods = 20 years
Plugging in the values, we have:
FV = $400,000 * (1 + 0.05)^20
Now, let's calculate the future value:
FV = $400,000 * (1.05)^20 = $400,000 * 2.6532977 ≈ $1,061,319.08
So, after 20 years, Simon's investment will grow to approximately $1,061,319.08.
Now, we need to find the maximum annual withdrawal Simon can make over the next 15 years. We divide the future value by the number of years he plans to withdraw (15 years):
Maximum Annual Withdrawal = FV / 15 years = $1,061,319.08 / 15 ≈ $70,754.60
Therefore, the maximum annual withdrawal Simon can make over the next 15 years is approximately $70,754.60.