Question

Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...

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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $112,331.00 from his retirement account until he turns 89.00. After this final withdrawal, he wants $1.49 million remaining in his account. 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 10.00% interest rate. (round to 2 decimals)

Homework Answers

Answer #1

Amount required on 74th birthday is equal to present value of future withdrawals

= 112,331*PVAF(10%, 15 years) + 1,490,000*PVF(10%, 15 years)

= 112,331*7.6061 +1,490,000*0.2394

= $1,211,106.8191

Amount required on 65th birthday = 1,211,106.8191/(1.10)9

= $513,627.52

Future value of Annuity = Periodic Amount*[{(1+r)n โ€“ 1}/r]

Let annual deposits be x

513,627.52 = x*[{(1.10)40 -1}/0.10]

513,627.52 = 442.592555x

X = $1,160.50

Hence, annual contribution required = $1,160.50

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $130,692.00 from his retirement account until he turns 88.00. After this final withdrawal, he wants $1.38 million remaining in his account. He...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $198,730.00 from his retirement account until he turns 91.00. After this final withdrawal, he wants $1.92 million remaining in his account. He...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $176,595.00 from his retirement account until he turns 92.00. He he will make contributions to his retirement account from his 26th birthday...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $105,528.00 from his retirement account until he turns 85.00. After this final withdrawal, he wants $1.36 million remaining in his account. He...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will wants to have $3,278,432.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
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 the day he turns 74.0 when he fully retires, he will begin to make annual withdrawals of $143,996.00 from his retirement account until he turns 92.00. He he will make contributions to his retirement account from his 26th birthday...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he...
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. 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 72.0 when he fully retires, he will begin to make annual withdrawals of $118,640.00 from his retirement account until he turns 89.00. After this final withdrawal, he wants $1.26 million remaining in his account. He...
9)#1 Derek plans to retire on his 65th birthday. However, he plans to work part-time until...
9)#1 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 $101,516.00 from his retirement account until he turns 90.00. He he will make contributions to his retirement account from his 26th...
A) Derek plans to retire on his 65th birthday. However, he plans to work part-time until...
A) Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 72.00. 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 72.0 when he fully retires, he will begin to make annual withdrawals of $120,165.00 from his retirement account until he turns 94.00. He he will make contributions to his retirement account from his 26th...
27. Derek plans to retire on his 65th birthday. However, he plans to work part-time until...
27. 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 $189,025.00 from his retirement account until he turns 89.00. He he will make contributions to his retirement account from his 26th...