Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 74.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after he fully retires on the day he turns 74.0, he will wants to have $3,027,667.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 6.00% interest rate.

Answer Format: Currency: Round to: 2 decimal places.

Answer 1

To reach his retirement goal, Derek must make contributions of approximately $9,599.03.

Step-by-step explanation:

To calculate the contributions Derek must make to reach his retirement goal, we can use the formula for the future value of an annuity: FV = P((1+r)^n - 1)/r, where FV is the future value, P is the periodic contribution, r is the interest rate, and n is the number of periods. In this case, Derek will make contributions from his 26th birthday to his 65th birthday, which is a total of 39 periods. The future value he wants to achieve is $3,027,667.00.

Plugging in the values, we have:

$3,027,667.00 = P((1+0.06)^39 - 1)/0.06

Simplifying the equation, we get:

P = $3,027,667.00 * (0.06/((1.06)^39 - 1))

Calculating this using a calculator, we find that Derek must make contributions of approximately $9,599.03 to reach his retirement goal.