Question

Derek plans to retire on his 65 th birthday. However, he plans to work part-time until he tums 73.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he tums 73.0 when he fully retires, he will wants to have $2,624.572.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65 th birthday. To reach his goal, what must the contributions be? Assume a 9.00% interest rate. Answer format: Currency: Round to 2 decimal places

Answer 1

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.