FIN 254Case 1

1. Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a xed re- tirement income that has the same purchasing power at the time he retires as $40,000 has today (he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Ination is expected to be 5 percent per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?

2. You are serving on a jury. A plaintiff is suing the city for injuries sustained after falling down an uncovered manhole. In the trial, doctors testied that it will be 5 years before the plaintiff is able to return to work. The jury has already decided in favor of the plain- tiff, and has decided to grant the plaintiff an award to cover the following items:(1) Recovery of 2 years of back-pay ($34,000 in 2000, and $36,000 in 2001). Assume that it is December 31, 2001, and that all salary is received at year end. This recov- ery should include the time value of money.(2) The present value of 5 years of future salary (20022006). Assume that the plaintiffs salary would increase at a rate of 3 percent a year.(3) $100,000 for pain and suffering. (4) $20,000 for court costs.Assume an interest rate of 7 percent. What should be the size of the settlement?

3. a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10 percent, compounded annually.b. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10 percent, compounded annually, and that the loan is paid off over 5 years.c. How large must each payment be if the loan is for $50,000, the interest rate is 10 percent, compounded annually, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?

4. Case from Gitman (Chapter 4 p-22) : Funding Jill Morgans Retirement Annuity

Good Luck!!!

1)As the inflation rate is 5% per year after 10 years if I want to buy the same thing that I can buy with $40000 then I need to have the following amount of money:FV = PV(1+k)n , Here, FV = money I need after 10 years to have the same purchasing power that has todays $40000k= inflation rate, n= yearsso, FV = 40000(1+.05)10 = $65155.79To have this amount after 10 years I need to save the following amount each year:

FVAn = PMT[] = PMT[] FVA= 65155.79n=10, k=8% (as the savings interest rate is 8%)

so, PMT = [] =[ ]PMT= PMT = $4497.671So, My father needs to save $4498 each year to have the same purchasing power that has todays $40000

2.)Future value of year 2000 salary = 34000(1+.07) = $36380value of year 2001 salary (current time) = $36000Future Salary of year 2002-2006 (salary increase 3% per year)200237080

200338192.4

200439338.172

200540518.31716

200641733.86667

36000 (1+.03) 37080(1+.03) 38192.4(1+.03) 39338.172(1+.03) 40518.31716(1+.03) Present value of year 2002-2006 salary=200234654.21

200333358.72

200432111.67

200530911.23

200629755.67

Total = $160791.5

(we need to use the unequal stream PV formula to find out the PV of this annuity)PV = PMT + PMT +PMT + PMT + PMT

PMT=each years salaryk= interest rateso, PV = 160791.4935So the total settlement amount =36800+36000+160791.5+100000(suffering cost)+20000(court fee)= $353171.5

YearBeginning AmountPaymentInterestRepayment of PrincipalRemaining Balance

Column 1Column 2Column 3Column 4 (column2-column3)Column 5 (column1-column4)

2012250006594.93725004094.93720905.063

201320905.0636594.9372090.5064504.430716400.6323

201416400.63236594.9371640.0634954.8737711445.75853

201511445.758536594.9371144.5765450.3611475995.397383

20165995.3973836594.937599.53975995.3972620.0001213

3-a)

Interest = 25000*0.1=2500, 20905.063*0.1=2090.506, 16400.6323*0.1=1640.063, 11445.75853*0.1=1144.576, 5995.397383*0.1=599.5397

PV of Annuity = PMT[ ]PV of annuity = 25000, k = 10%=0.1, n= 5, PMT=payment=?So, payment = = $6594.9373-b)Payment = payment = =$13189.87404PV of annuity = 50000, k = 10%=0.1, n= 5, PMT=payment=?

3-c) Payment = payment = = $8137.269744Here, PV of annuity = 50000 and n=10The amount is not as half as part b because of the present value interest factor

4)To answer this question I must find the present value of the annuity for next 25 years.So, PVAn = PMT[] = PMT[]= PMT[]Here, PVAn= present value of the annuity = amount I am willing to pay for this retirement plank= interest rate = 9%, n=25 years, PMT=$12000

so, PVAn= 12000[]= 12000* 9.82258= $117870.9553So, I would like to pay $117870.9553 for this retirement plan.