Question 1203101
The given parameter are;

{{{P[o]}}}= The principal or initial balance in the account at the beginning


{{{d }}}= The amount to be withdrawn each year ={{{d=30000}}}

{{{r}}} =  The interest rate per annum ={{{ 8}}}%=>{{{r=0.08}}}

{{{k }}}= The number of periods the interest is applied in a year = {{{k=1}}}

{{{n}}} = The number of years withdrawal is made ={{{n= 25}}}


a. The amount that should be in the account at the beginning is given by the payout annuity formula as follows;


{{{P[o]=(d(1-(1+r/k)^(-nk)))/(r/k)}}}


substitute given values and we get:


{{{P[o]=(30000(1-(1+0.08/1)^(-25*1)))/(0.08/1)}}}

{{{P[o]=(30000(1-(1.08)^(-25)))/(0.08)}}}

{{{P[o]=25619.462852612596/0.08}}}

{{{P[o]=320243.3}}}



The amount needed in the account at the beginning, 

{{{P[o] =320243.3}}}


b. The amount of money pulled out,

{{{ A = n*d}}}

Therefore, 

{{{A = 25*30000=750000}}}


c. The amount of money received as interest, 

{{{I = A - P[o]}}}

 {{{I = 750000 - 320243.3 = 429756.7}}}