Answer:the required contributions for Derek to reach his retirement goal would be approximately $16,070.48 per year.To calculate the required contributions for Derek to reach his retirement goal of $3,041,029.00, we need to consider the timeframe from his 26th birthday to his 65th birthday. This gives us a period of 39 years.
Step-by-step explanation:Using the future value of an ordinary annuity formula, we can calculate the required contributions. Plugging in the values:
- Future value (FV) = $3,041,029.00
- Interest rate (r) = 4.00% (expressed as 0.04)
- Number of periods (n) = 39
The formula for calculating the required contributions (PMT) is:
PMT = FV / [(1 + r)^n - 1] * (r / (1 + r))
Substituting the values into the formula, we get:
PMT = $3,041,029.00 / [(1 + 0.04)^39 - 1] * (0.04 / (1 + 0.04))
After calculating this, the required contributions for Derek to reach his retirement goal would be approximately $16,070.48 per year.