Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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

Sagot :

Answer:

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.

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.