You want to retire in 38 years and have $100,000 currently saved in an account earning 9.5% interest. How much must you deposit into that account each month to be able to retire for 25 years and withdraw $500,000 per year if you are able to earn 5% during retirement?
Annuity Withdrawl Required (P)=  500000 
interest rate (i)=  5% 
time for Annuity withdrawl (n)=  25 
Present Value of ordinary annuity formula = (Annuity *(1(1/(1+i)^n))/i) 

=500000*(1(1/(1+5%)^25))/5% 

=7046972.283  
So fund needed at Retirement is  $7046972.28 
Current deposit (present value) =  100000 
interest rate (i)= 9.5% number of years (n) = 38 future value = present value *(1+i)^n =100000*(1+9.5%)^38 =3145839.264 

Ballance Future value required to be saved =7046972.28 3145839.26  3901133.02 
Time in years (n) =  38 
interest rate (i)=  9.5% 
Amount required to save each year Formula = Future value*i/(((1+i)^n)1) 

3901133.02*9.5%/(((1+9.5%)^38)1) 

12167.6689  
So annual Contribution needed is  $12167.67 
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