Question 1108784
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:


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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.