If upon retirement in 20 years Greg plans to invest 800,000 in a fund that earns 4 percent, What is the maximum annual withdrawal he can make over the following 15 years
To calculate the maximum annual withdrawal Greg can make over the next 15 years, we need to use the formula for calculating the future value of an investment:
Future Value = Present Value × (1 + Interest Rate)^(Number of Periods)
Given that Greg plans to invest $800,000 at an interest rate of 4 percent for 20 years, we can calculate the future value:
Future Value = $800,000 × (1 + 0.04)^(20) = $1,516,393.66 (rounded to two decimal places)
Now, we need to calculate the maximum annual withdrawal over the next 15 years. Assuming Greg wants to deplete the investment by the end of the 15-year period, we can divide the future value by the number of years:
Maximum Annual Withdrawal = Future Value / Number of Years = $1,516,393.66 / 15 = $101,092.91 (rounded to two decimal places)
Therefore, the maximum annual withdrawal that Greg can make over the next 15 years is approximately $101,092.91.
To determine the maximum annual withdrawal Greg can make over the next 15 years, we need to use the concept of a retirement fund and the concept of compound interest.
First, we need to calculate the future value of the $800,000 investment after 20 years at a 4% annual interest rate. This can be achieved using the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate) ^ Time
Future Value = $800,000 * (1 + 0.04) ^ 20
Future Value = $800,000 * (1.04) ^ 20
Future Value = $800,000 * (1.816)
Future Value = $1,452,800
So, after 20 years, Greg's investment will grow to $1,452,800.
Now, we can calculate the maximum annual withdrawal Greg can make over the next 15 years with this amount.
Since Greg wants to make withdrawals over 15 years, we divide the future value by 15. This will give us the maximum annual withdrawal amount:
Maximum Annual Withdrawal = Future Value / Number of Years
Maximum Annual Withdrawal = $1,452,800 / 15
Maximum Annual Withdrawal ≈ $96,853.33
Therefore, the maximum annual withdrawal Greg can make over the following 15 years is approximately $96,853.33.