You have just retired and reached your objective (see above) of accumulating $3,500,000 in your retirement fund. You expect to live for another thirty years (exactly) and wish to leave $1,000,000 to the Chicago Symphony Orchestra (CSO) when you are gone. What is the most that you could withdraw from this fund at the end of each quarter and still leave the money to the CSO? The fund is expected to return six percent per annum, compounded monthly?

Quarterly Payments = R=$45,046.66

Explanation:

55.498

Accumulated Amount At retirement = $3,500,000

Amount to be left for CSO                 = $1,000,000

Net Cash That Can be utilized          =  $2,500,000

Quarterly Payments = ?

Total Quarterly Payments = 30*4 = 120

Interest Annual  = 6% = 6/4 = 1.5% Quarterly

Present Amount =$2,500,000

We will solve it by by annuity Formula i.e P=R(1-(1+i)^-n)/i

So We have= 2,500,000=R(1-(1+1.5%)^-120)/1.5%

                    = 2,500,000=R(1-0.167)/1.5%

                    =2,500,000=R* 0.8325/1.5% =

                    =2,500,000=R* 55.498 =

                     R=2,500,000/55.498

                     R=$45,046.66

most Quarterly payment that can be with drawl is R=$45,046.66/-

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