Question

Explain the change in the cash balance from $668 million to $297 million by showing the effect of operating activity, investment activity, and financing activity.

Answer 1

Amount need to be saved till retirement (Future value) = 1000000

Deposit per quarter (P) = $1000

Rate of return is 12% compounded quarterly

 

 So quarterly rate of return (i) = Annual rate/quarters in year

                                                     =12%/4

                                                     =3%

 

We will use future value of annuity formula to calculate number of years needed to accumulate $1000000

 

Future value of annuity formula = P*(((1+i)^n)-1)/i

1000000 = 1000*(1+3%)^n)-1)/3%

 

We will use trial and error method and interpolation formula to calculate the number of periods to accumulate $1000000. N is the number of quarters in which given amount will be accumulated

 

Assume n = 115 quarters

FV =1000*(((1+3%)^115)-1)/3%

     =964733.4139

 

Assume n=118 quarters

FV = 1000*(((1+3%)^118)-1)/3%

     = 1057281.149

 

Interpolation formula = Upper n -((Upper n-lower n)/(Upper value - lower value)*(Upper value - actual value))

                                        = 118-((118-115)/(1057281.149-964733.4139)*(1057281.149-1000000))

                                        = 116.1431912

 

In years = Total quarters/Quarters in a year

               = 116.1431912/4

               = 29.0357978

 

So we have to wait 29.04 years to retire.

So we have to wait 29.04 years to retire.