Question

1. You aunt has just retired and has $5,000,000 in her retirement account. She expects to live for another thirty years (exactly) and wishes to leave $600,000 each to the Chicago Symphony Orchestra, Lyric Opera of Chicago and Illinois Tech when she is gone. What is the most that she could withdraw from this account at the end of each quarter and still leave the money to her desired beneficiaries? The fund is expected to return six percent per annum, compounded monthly?

Answer 1

As there are 30 years and quarterly payment so number of periods=4*30=120
Rate compounded quarterly=((1+rate compounded monthly/12)^(12/4)-1)*4=((1+6%/12)^(12/4)-1)*4=6.03%
Amount withdrawn each quarter

Using formula:
=(present value-future value to be left/(1+quarterly compounded rate/4)^(4*number of years))/(1-1/(1+quarterly compounded rate/4)^(4*number of years))*(quarterly compounded rate/4)
=(5000000-600000/(1+6.03%/4)^(4*30))/(1-1/(1+6.03%/4)^(4*30))*(6.03%/4)=88582.11

Using Microsoft Excel
=PMT(6.03%/4,4*30,-5000000,600000)=$88,582.11

Using Financial Calculator:
N=4*30=120
FV=600000
PV=-5000000
I/Y=6.03%/4
CPT PMT=88582.11