Sam intends to retire after four years of work. Once he retires, he will need to

Question

Sam intends to retire after four years of work. Once he retires, he will need to withdraw S50,000 at the beginning of the first, second and third year of retirement. After that he will die. How much must he invest now, assuming an interest rate of 12% to achieve such a cash flow? k. Stephen Bosworth, a super salesman contemplating retirement on his fifty-fifth birthday, decides to create a fund on an 8% basis that will enable him to withdraw $25,000 per year on June 30, beginning in 2014 and continuing through 2017. To develop this fund, Stephen intends to make equal contributions on June 30 of each of the years 2010-2013. How much must the balance of the fund equal on June 30, 2013, in order to satisfy his objective?

Explanation / Answer

j.

here,

first we will calculate the present value of annuity sam will receive at fourth year

Present value =Annuity*((1+r)^-n)/r)= 50000*((1.12^-3)/0.12)

=120091

then we will discount this value to present to find out the amount sam needs to invest

=(120091/1.12^4)

=76320

k.

stephen will receive 25000 every year from 2014 till 2017

first using present value of annuity we will discount this amount find present value at 2014

at 2014,

Present value =Annuity*((1+r)^-n)/r)=25000*((1.08^-3)/0.08)

=248072.57

now we discount this amount for one year,

value required=248072.57/1.08=$229696.82

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