Question

$____________5. Your brother knows you are taking CMP325 and are fast becoming a financial genius. He...

$____________5. Your brother knows you are taking CMP325 and are fast becoming a financial genius. He plans to retire when he is 55 years old; today is his 18th birthday. If he plans to accumulate $1,000,000 for retirement, how much must he deposit each year in order to reach his goal if his investment will pay 8% interest per year compounded annually?

Homework Answers

Answer #1

The question belongs to Annuity Due.

The formula for Annuity Due:

Future Value of Annuity = Annuity *[ { (1+ rate ) n - 1 } / rate ] * ( 1 + r )

Given:
Rate: 8%
n= 37 years ( 55 years - 18 years)
Future Value of Annuity = $ 1,000,000

Now,

1,000,000 = Annuity * [ { ( 1+0.08 ) 37 - 1 } / 0.08 ] * ( 1+ 0.08 )
1,000,000 = Annuity * [ { ( 1.08 ) 37 - 1 } / 0.08 ] * 1.08
1,000,000 = Annuity * [ { 17.24 - 1 } /1.08 ] * 1.08
1,000,000 = Annuity * [ 16.24 / 1.08 ] * 1.08
1,000,000 = Annuity * [ 203 ] * 1.08
1,000,000 = Annuity * 219.24
Annuity = 1,000,000 / 219.24
Annutiy = $ 4561.21

So, he must deposit $ 4561.21 each year in order to reach his goal.

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
Assume that your brother is now 50 years old, that he plans to retire in 10...
Assume that your brother is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires (i.e. until he is 85 years old). He wants a fixed retirement income that has the same purchasing power at the time he retires as $50,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin...
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 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 turns 73.0 when he fully retires, he will wants to have $3,423,684.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his...
Your older brother turned 35 today, and he is planning to save $20,000 per year for...
Your older brother turned 35 today, and he is planning to save $20,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year...
Newman Hitchcock is 38 years old today and he wishes to accumulate $501,000 by his 61st...
Newman Hitchcock is 38 years old today and he wishes to accumulate $501,000 by his 61st birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 38th through his 60th birthdays. What annual deposit must Newman make if the fund will earn 8% interest compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)
Vincent would like to have $50,000 per year to live off in his retirement. He expects...
Vincent would like to have $50,000 per year to live off in his retirement. He expects to retire on his 65th birthday, make his first retirement withdrawal on his 66th birthday, and to live until his 85th birthday. He is celebrating his 30th birthday today and will make his first savings deposit one year from today. If he can earn 4% per year on his savings, the amount he must save each year to meet his goal, with the last...
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 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 wants to have $3,397,041.00 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 71.00. 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 71.0 when he fully retires, he will wants to have $2,847,993.00 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 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 turns 73.0 when he fully retires, he will wants to have $3,310,550.00 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 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 wants to have $2,823,229.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his...