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Thus problem is related to compound interest calculations, but with a twist: regular withdrawals are to be taken into account and they will reduce the principal over the years. The problem consist in determining which is the principal - P or P(0) - that one should have accumulated at age 60 in order to retire an live up to 90 (that is, the period is 30 years) with yearly withdrawals of 72000. A fixed yearly interest rate of 8% (or 0.08 if expressed in decimals) is considered. After 30 years (age 90) the accumulated savings should be zero.
After the first year, the total amount of savings is P(1)=P(0)*(1+0.08)^1-72000
This can be generalized for any given time period as P(n)=(P(0)*(1+0.08)^n) - ((1.08^n)-1)(72000/0.08)
The answer to the problem can be found by solving for n=30 and P(n)=0
It is possible to find P(0)=$ 810565, according to rounding up or down during calculations.
This calculation considers, for the sake of simplicity, one yearly credit of interests (8%) and a single yearly withdrawal of $72000. Also, interests are calculated as credited at the end of 30th year.
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