time 40. You want to retire at age 65, you begin your investment program at 25 w
ID: 2615986 • Letter: T
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time 40. You want to retire at age 65, you begin your investment program at 25 with a one deposit of $5,000 in a traditional IRA on this investment you can earn 1 190 in the Vanguard 2055 retirement fund. At age 35 you come into an inheritance of $15,500 of which you decide to put into a Roth IRA, using a Fidelity index fund which you anticipate will yield 9.5% until 65, At 45 you remember taking Elliott's class and listening to Bryan Washburn and Mark Russell and you realize that you have $14,000 extra saved for retirement. To be super safe you invest this sum in another Roth IRA which you will receive a 7% return. At 65 you want to retire at $120,000,gross a year for 30 years, (you need this much because you didn't factor in Inflation, (Elliott was too nice and didn't want you be depressed) and you anticipate you can earn 4% on the payout or annuity, not perpetuity. (PartA) With all of this information, and it is not too much into how much will you need to invest each year at 10%. beginning at 25 to 65, using a mutual fund, traditional IRA account to achieve your retirement goal of $120,000 gross for 30 years? (4 points),part A. (this must mean that you were still short of funds from the other investments) The second part: (Part B) remember Bryan Washburn and Mark Russell indicated we are looking for tax-free income at retirement, and thus, you are the 25% tax bracket at retirement, how much will you net each year in retirement, after taxes? (4 points), (Part B.)Explanation / Answer
Part A:
In this part, we first need to determine total funds requirement at the time of retirement that would enable annual payments of $120,000 for 30 years. For this, we will use annuity payment formula given below:
P = (r*PV) / [1 – (1+r)-n]
Where:
P = Annuity payment every year = $120,000
r = Rate per period = 4% or 0.04
PV = Amount at the time, when annuity payout starts (This needs to be calculated)
n = Number of annuity payments = 30
Calculation of funds required:
$120,000 = (0.04*PV) / [1-(1+0.04)-30]
$120,000 = (0.04*PV) / (1 - 0.308318668)
($120,000 * 0.691681332) = (0.04*PV)
PV = ($120,000 * 0.691681332) / 0.04 = $2,075,044.00
So, the amount required at the time of retirement to receive annuity payments of $120,000 for 30 years is $2,075,044
Now, we would need to calculate the value of all investments done at the time of retirement as it will enable us to know the shortfall. Below given formula is used to calculate future value.
Future value of a single deposit: FV = Amount * (1+r)n
Future value of $5,000 deposited when you were 25 = $5,000 * (1+0.11)40 = $325,004.34
Future value of $15,500 deposited when you were 35 = $15,500 * (1+0.095)30 = $235,914.85
Future value of $14,000 deposited when you were 45 = $14,000 * (1+0.07)20 = $54,175.58
Total amount available at the time of retirement = $325,004.34 + $235,914.85 + $54,175.58 = $615,094.77
Shortfall = $2,075,044 - $615,094.77 = $1,459,949.23
Now we need to determine the annual deposits required to accumulate $1,459,949.23 in 40 years at a rate of 10%. For this, we will use the formula of Future value of annuity due.
FV of annuity due = C*{[(1+r)n-1] / r} * {1+r}
Where,
FV = $1,459,949.23
C = Annual deposit required to accumulate the future value (This needs to be calculated)
r = Rate of interest = 10% or 0.10
n = Number of periods = 65 Years – 25 Years = 40
Putting the values in formula:
$1,459,949.23 = C*{[(1+0.10)40 – 1] / 0.10} * {1+0.10}
$1,459,949.23 = C* {44.25925557 / 0.10} * {1.10}
C = $1,459,949.23 / (442.5925557*1.10)
C = $2,998.75
So, you would need to make an annual deposit of $2,998.75 on top of all other investments made to receive $120,000 annually for 30 years.
Part B:
After-tax income = Pre-tax income * (1-tax rate)
=> $120,000 * (1-0.25) = $90,000
So, you will net $90,000 each year in retirement after taxes.
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