You have been asked by a client to prepare a savings schedule
consitent with her retirement plan.  Your client gives you the
following information.  Today is her birthday.  She just turned 25. 
She wants to retire when she is 65 and she expects to live until 80. 
Beginning her 66th birthday she wants to withdraw annually $50,000
from her retirement account until (and including) her 80th birthday. 
Beginning next month and ending on her 65th birthday she wants to make
monthly deposits that would ensure that she is able to withdraw the
desired amount during her retirement.  If the interest is 10% APR how
much would she have to deposit each month?

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Request for Question Clarification by elmarto-ga on 15 Dec 2004 13:14 PST

Hi tdjii,
Are you still interested in paying for a complete answer to this question?

Best regards,
elmarto

<I?m assuming by 10% APR you mean compounded annually>

From end of 65 (beginning 66) to end of 79 (beginning 80) is 19 yrs

N = 19
I = 10
50,000 = PMT

PV = 418, 246  <- she needs to have saved 


From end of 24 (beginning 25) to end of 65 (beginning 66) is 41 yrs
10 % per year is 9.569 % compounded monthly  
 
N = 41*12
I = 9.569/12
FV = 418, 246  

PMT =   68.36

So she needs to save this much per month.

From end of 65 (beginning 66) and it is supposed to include 80 so that
would be a total of 15 years, not 19 years.

Secondly,
   Where does the 9.569% come from?

Yes, your comment on the number of years is correct.  I typed 19 instead of 14.

As I said above, *I?m assuming by 10% APR you mean compounded annually*

ie If 10% is the *annual* compounded rate (1 compounding period), this
converts to a 9.569 % compounded monthly rate (12 compounding
periods).

Conversely, if the 10% is a *monthly* compounded rate, this converts
to an effective annual rate of 10.47% which should be used instead of
10% in the calculation of how much she needs to have saved by 65.