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: 30
Amount to withdraw each year: $90,000
Years to withdraw in retirement: 20
Interest rate: 8%
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: $ 1,500
Years until trust fund distribution: 20
Amount of trust fund distribution: $25,000
Guide On Rating System
Vote
a. To calculate the amount your friend must deposit annually, we can use the future value of an ordinary annuity formula.
FV = P * ((1 + r)^n - 1)/r
Where:
FV = Future value (the desired withdrawal amount each year in retirement)
P = Annual deposit
r = Interest rate (8% or 0.08)
n = Number of years until retirement (30)
Using the given information, we can substitute the values into the formula:
$90,000 = P * ((1 + 0.08)^30 - 1)/0.08
To solve for P, we rearrange the equation:
P = $90,000 * 0.08 / ((1 + 0.08)^30 - 1)
By plugging the values into the equation, we can calculate the annual deposit:
P = $90,000 * 0.08 / ((1.08)^30 - 1)
P ≈ $2,338.48
Therefore, your friend must deposit approximately $2,338.48 annually to be able to make the desired withdrawals at retirement.
b. To calculate the lump-sum deposit your friend must make today, we can use the future value formula.
FV = P * (1 + r)^n
Where:
FV = Future value (the desired withdrawal amount each year in retirement)
P = Lump-sum deposit
r = Interest rate (8% or 0.08)
n = Number of years until retirement (30)
Using the given information, we can substitute the values into the formula:
$90,000 = P * (1 + 0.08)^30
To solve for P, we rearrange the equation:
P = $90,000 / (1 + 0.08)^30
By plugging the values into the equation, we can calculate the lump-sum deposit:
P = $90,000 / (1.08)^30
P ≈ $17,372.24
Therefore, your friend must make a lump-sum deposit of approximately $17,372.24 today to cover her retirement needs.
c. To calculate the amount your friend must deposit annually considering the employer's annual contribution and the trust fund distribution, we need to adjust the annual deposit amount.
The adjusted annual deposit would be the desired withdrawal amount minus the employer's contribution and the expected trust fund distribution. Therefore:
Adjusted annual deposit = Annual deposit - Employer's contribution - Trust fund distribution
Using the given values:
Adjusted annual deposit = $2,338.48 - $1,500 - $25,000
Adjusted annual deposit ≈ -$23,161.52
Since the result is negative, your friend doesn't need to deposit anything annually considering the employer's contribution and the expected trust fund distribution. The employer's contribution and the trust fund distribution cover more than the desired withdrawal amount.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99