Question 1108784: You have $100000 to invest at 4% interest.if you wish to withdrawal equal annual payments for 4 years, how much couid you withdrawal each year and leaves $0 in the investment account?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 100,000 is invested at 4% interest peryear.
you wish to withdraw money at the end of each year, for 4 years and have 0 in the account at the end of the fourth year.
your withdrawal amount would be equal to 27,549.00454 each month.
the year by year calculations are shown below:
the calculation of the withdrawal was done using the TI-BA-II financial calculator.
in this calculator, the entries were made as follows:
N = 4
I/Y = 4 (% is assumed by the calculator).
PV = -100,000 (no comma)
FV = 0
then 2nd PMT gets you the withdrawal amount.
the calculator shows the withdrawal as 27,549.00454.
that's a rounded number.
the actual number goes out for more digits.
the excel printout uses a similar formula, only it carries out the result to more decimal digits.
the formula in excel is =PMT(rate,nper,pv,[fv],[type])
if fv is 0 and type is end of time period payments/withdrawals, then the formula used can be PMT(rate,nper,pv), which is what i used, because fv is assumed to be 0 and end of time period payments are assumed.
there is also a manual formula that can be used to calculate the withdrawal.
that formula is shown below:
ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS
a = (p*r)/(1-(1/(1+r)^n))
a is the annuity.
p is the present amount.
r is the interest rate per time period.
n is the number of time periods.
with this formula:
a is what you want to find.
p is the present amount = 100,000 (without the comma).
r is the interest rate per year = .04 (not the interest rate percent).
n is the number of year = 4
formula of a = (p*r)/(1-(1/(1+r)^n)) becomes:
a = (100000*.04)/(1-(1/(1+.04)^4))
solve for a to get a = 27549.00454.
when you enter the formula in your calculator, make sure the parentheses are entered exactly as shown in the formula.
your solution, rounded to 2 decimal digits, is that you would withdraw 27,459.00 at the end of each year.
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