Anyone one want to take a shot at this question? If so, please comment to this post.
True story: Last night, I was helping my wife's 24 year old brother set-up his first retirement account, a Roth IRA (Individual Retirement Account). We estimated that he will retire when he is age 67 and he will invest his first contribution of $5,000 in one year (we just set-up the account and did the paper work). He will make annual contributes of $5,000 per year until retirement (note: $5,000 is currently the maximum you can contribute to an IRA). We selected an account that is a mix of stocks and bonds (but primarily stocks). The long-term average return on this account is 9%, which we thought was an appropriate return or rate for our analysis.
How much will my wife's brother have at age 67? Of this amount, how much is interest on principle? How much is compound interest? How much did he actually deposit into this account?
Wednesday, January 30, 2008
Extra TVM problem...
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4 comments:
Here goes my attempt (let me know if I am wrong):
It is estimated that our professor’s brother-in-law hopes to retire in the year 2051 (forty-three years from now), at which time he will be sixty seven years of age. Any IRA is a good choice, but a Roth is particularly good for tax purposes, if you are concerned about the tax consequence of withdraws. Specifically, on a Roth IRA, contributions are not tax deductible, but any growth is tax free and qualified withdrawals may be tax free although he must keep in mind that certain holding periods and income restrictions apply. Basically in selecting your type of IRA you must ask yourself, “Do I want to pay my income tax now or later?” The lower your tax bracket today, the more likely a Roth IRA will be to your advantage and the younger you are, the more likely a Roth IRA will be to your advantage.
A physical amount of 215 thousand dollars will actually be deposited in the retirement account which actually holds a present value of $ $73,474.28 if your estimate of a constant 9% yield holds true. Upon retirement this amount will have a future value of $2,204,228.32.
Don’t pick out the Bentley yet! You are by no means going to be living the life of the rich and famous! The average American male today lives until the age of seventy-two, but living until his nineties is increasingly common. My point is, that the 2.2 million dollars may seem like a ton of money, however if he lives until he is ninety seven, this money has to last him thirty years! Don’t forget, inflation rises at an average of three percent annually, so that number decreases even further.
Lucky for him a little under eighty thousand (very rough guesstimate) a year is what it should come out to live the average American lifestyle. That is if he doesn’t suffer any significant medical ailments as our elderly population usually does (his next step should be to secure solid long term health care coverage).
Calculations:
If using the formula (Fx) function you with enter =FV(rate, number of periods, payment amount, present value and timing of payment). For this problem that is: =FV(0.09,43,5000,0,0).
Cora has got the total contribution of $215,000 ($5,000 x 43) and FV of $2,204,228.33 correct (good job!). To show our work, let's use the calculator key strokes method (remember, you won't have Excel for the exam).
n=43
i=9
pv=0
pmt=-5000 (I used a negative because it is a cash outflow)
fv= solve: 2,204,228.33
But, how much of this total FV is interest and how much is compound interest (interest on interest)?
Not done yet... (Anyone? Anyone? Bueller..)
Well lets if i can give it a try.
To find out how much of the FV is interest just subtract the $2,204,228.32 from $215,000 the amount your brother-in-law deposited which would give you
$2,204,228.32 - $215,000 =
$1,989,228.32
to find the compound interest you use the calculator
FV= $1,989,228.32
i= 9%
n= 43
PMT= $4,512.30 a year
We can do a quick approximation calculation of the interest on the principle deposited ($215,000) by taking $215,000 x .09 = $19,350.
If we figured out that the total amount of interest (interest on principle and compound interest)was $1,989,228.32. This amount less the interest on principle ($19.350) is $1,969,878.32 which shows the power of compound interest. The majority of the interest is compound interest or interest on interest.
The key to compounding interest is really the number of compounding periods (and of course the interest rate is important). Try this problem again but this time use a variety of compounding periods (n). Try n= 5, 10, 20, 30, etc. The point of this exercise should be "START YOUR IRA OR OTHRER RETIREMENT ACCOUNT AS EARLY AS POSSIBLE!"
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