Annuties Help (I don't need an answer to the problem jsut help on which formula to use)?

Question

You would like to collect 3500 each quarter for 10 years after you retire and you can set up this annuity in a n account that pays 12% compounded quarterly. how much will you need at the beginning of your annuity?

Feedback is greatly appreciated!!!

Answer 1

If made an initial deposit "D0" and each quarter thereafter you  withdrew "T" amount

'n'   number of quarters

'i'   interest rate per quarter i.e. 12% APR use 0.12/4

'D0'  initial deposit

'T'   withdrawel at beginning of each quarter starting on 2nd quarter

    

Balance after 'n' quarters with 'T' withdrawal each quarter

Bal(n) =  D0*(1+i)^n + T*( (1 - (1 + i)^n) / i) - 1)

set 'n' = 10*4 = 40 quarters

set Bal(n) = 0

solve for D0