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Question 423416: I am 30 years old and want to retire at age 60. I want to be able to collect $60,000 a year for 20 years. At 5% interest, how much money do I need to invest today to be able to collect $60,000 for 20 years by the time I reach 60?
Thank you in advance for any help and/or consideration. This one is really stumping me because I do not even know what formula to use.
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you will be retiring in 30 years (60 - 30 = 30)
you want to be able to collect $60,000 a year for 20 years.
since you normally collect the money monthly, i'll assume the following:
5% per year compounded monthly is equivalent to .416666667% per month.
$60,000 per year is equivalent to $5,000 a month.
since you want to collect for 20 years, that's equivalent to 240 months.
the present value of $5,000 monthly at .4166666667% per month for 240 months is equal to $757,626.5654
That's the amount of money you would need to have in the account at the beginning of your retirement period.
in order to have that much money in your account 30 years from now, you would need to invest $169,576.9749 today at 5% annual interest compounded monthly.
the formulas you will need at the present value of a payment formula.
this is also called the present value of an annuity.
you also need the present value of a future amount formula.
the formulas you require are shown below:
PRESENT VALUE OF A PAYMENT
PV = Present Value
PMT = Payment per time period
i = Interest Rate per Time Period
n = Number of Time Periods
PRESENT VALUE OF A FUTURE AMOUNT
PV = Present Value
FA = future amount
i = Interest Rate per Time Period
n = Number of Time Periods
since you will be compounding monthly, you need to make some adustments to the number of time periods and the interest rate per time period.
for the present value of a payment formula:
i = .05 / 12 = .004166667
n = 20 * 12 = 240
pmt = 60000 / 12 = 5000
for the present value of a future amount formula:
i = .05 / 12 = .004166667
n = 30 * 12 = 360
the present value of a payment formula will get you to $757,626.5654
that's the amount you have to have in the account 30 years from now.
the present value of a future amount formula will get you to $169,576.9749.
that's the amount you will need to invest today.
some references you might find useful are shown below:
http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson
Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! I'm not really sure how to read this, but I
think what they mean is:
Out of the 30 years I have before retirement,
I want to earn $60,000/yr for 20 of those
years. So, for the first 10 years I would
reinvest all the money and on the 11th year,
I would draw out exactly $20,000, and keep
drawing the same amount out for 20 years.
To find the minimum I must start with, I've
got to assume that ,on the 30th year, I will
exhaust all my investment.
So, the 1st part of the equation is  dollars
initial investment + reinvested principle and
interest over 10 years.
Let  = amount after 10 years
 (simple interest formula)
So, after 10 years I must have 
I need to invest $800,000 today.
I hope either or both the explanation and solution are helpful.
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