Question 6: This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals:
Years until retirement |
35 |
Amount to withdraw each year |
$85,000 |
Years to withdraw in retirement |
25 |
Interest rate |
7.5% |
Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account for her retirement fund.
a) If she starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?
b) Suppose your friend just inherited a large sum of money. Rather than making equal annual payments, she decided to make one lump-sum deposit today to cover her retirement needs. What amount does she have to deposit today?
c) Suppose your friend's employer will contribute to the account each year as part of the company's profit-sharing plan. In addition, your friend expects a distribution from a family trust several years from now. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?
Employer’s annual contribution |
$1,300 |
Years until trust fund distribution |
15 |
Amount of trust fund distribution |
$20,000 |
Base case:
PMT | $ 85,000.00 |
r | 7.50% |
n | 25 |
frequency | 1 |
r | 7.50% |
n | 35 |
T | 1 |
FV | $ 9,47,790.40 |
Part a) Now considering that she withdraws at the same pace however starts depositing one year later, the accumulated amount required is the same, however, the period for which deposits are made is reduced by 1 si annually she needs to deposit higher amount:
We are given the following information
r | 7.50% |
n | 34 |
T | 1 |
FV | $9,47,790.40 |
We need to solve the following equation to arrive at the
required FV
So annual PMT = $6,648.38
Part b) Here we basically find the PV of the required amount after 35 years so that is calculated below:
We are given the following information
r | 7.50% |
n | 35 |
frequency | 1 |
FV | $ 9,47,790.40 |
We need to solve the following equation to arrive at the
required PV
So the lumpsum to be deposited today will be 75407.76
C)
PMT | $ 1,300.00 |
r | 7.50% |
n | 35 |
T | 1 |
PV | 20000 |
r | 7.50% |
n | 35-15 = 20 |
frequency | 1 |
r | 7.50% |
n | 35 |
T | 1 |
FV | $ 6,62,006.29 |
Question 6: This is a classic retirement problem. A friend is celebrating her birthday and wants...
This is a classic retirement problem. A friend is celebrating her birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals: Years until retirement 35 Amount to withdraw each year $85,000 Years to withdraw in retirement 25 Interest rate 7.5% Because your friend is planning ahead, the first withdrawal will not take place until one year after she retires. She wants to make equal annual deposits into her account...
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Your best friend Dave just celebrated his 24th birthday and wants to start saving for his anticipated retirement. Dave plans to retire in 36 years and believes that he will have 25 good years of retirement and believes that if he can withdraw $125,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Dave for all scenarios presented below is 6.5% per year. This is an annual rate, review each...
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Your best friend Dave just celebrated his 24th birthday and wants to start saving for his anticipated retirement. Dave plans to retire in 36 years and believes that he will have 25 good years of retirement and believes that if he can withdraw $125,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Dave for all scenarios presented below is 6.5% per year. This is an annual rate, review each...
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Your best friend Dave just celebrated his 24th birthday and wants to start saving for his anticipated retirement. Dave plans to retire in 36 years and believes that he will have 25 good years of retirement and believes that if he can withdraw $125,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Dave for all scenarios presented below is 6.5% per year. This is an annual rate, review each...
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