Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 70.00. 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 turns 70.0 when he fully retires, he will begin to make annual withdrawals of $195,078.00 from his retirement account until he turns 94.00. After this final withdrawal, he wants $1.37 million remaining in his 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

X = $25,717.13 is the contribution amount that Derek has to plan.

Explanation:

Solution:

Assumption = Interest rate = 4%

Amount required at the age of 70 = value of all withdrawals

So, he will be making withdrawals until 94 years of age.

94 - 70 = 24

Annual Withdrawals = $195,078.00

Interest Rate = 4%

Period = 24 years.

Putting these values into the PVAF function, you will get:

PVAF(4%,24 years) = 15.24

So,

Amount required at the age of 70 = $195,078 x 15.24

Amount required at the age of 70 = 2972988.72

And now, we need to find the amount needed at the age of 65.

Amount required at the age of 65 = Present Value at the age of 65

Amount required at the age of 65 = 2972988.72 x PVF (4%,5 years)

PVF (4%,5 years)  = 0.822

Amount required at the age of 65 = 2972988.72 x 0.822

Amount required at the age of 65 = $2443796.72

Let suppose, annual contribution = x

X*[{(1+0.04)40-1]}/0.04] = $2443796.72

95.026X = $2443796.72

X = $25,717.13 is the contribution amount that Derek has to plan.