Reference no: EM132468210

Problem 1: Your uncle died last year and left you money in his will. You are to receive $100,000 in two years (time 2) and $1,000,000 eight years from today (i.e., in time 8).

(a) What is the value of the inheritance today (in time 0) if the appropriate discount rate is 5% compounded annually?

(b) If you invest the money when you receive it, how much will it grow to 40 years from today (i.e., in time 40) if you earn 5% compounded annually?

Problem 2: Your neighbor is buying a new Tesla electric car. He has the following options to finance the purchase:

I. Pays $35,000 today (in time 0) and $40,000 in one year (time 1)

II. Make payments under an increasing schedule as follows:

Time 0                         $10,000

Time 1                         $12,000

Time 2                         $14,000

Time 3                        $16,000

Time 4                         $18,000

Time 5                         $20,000

III. Make 78 monthlypayments over 6 years of $1,200 payable at the end of each month.

(a) If the interest rate is 6% annually, calculate the present value of each option.

(b) At what interest rate do Option II and Option III have the same present value?

Problem 3: A family friend is planning her retirement from work in the U.S. She is 62 years old right now (time 0) and has the choice of taking her Social Security (a public pension program) in time 0, in time 4 or in time 8 according to the following schedule:

I. Early retirement (Age 62 exactly)                    $1,400 per month for life

II. Regular retirement (Age 66 exactly)               $1,800 per month for life

III. Delayed retirement (Age 70 exactly)             $2,300 per month for life

If her expected life expectancy is 90 years old (exactly), what are the present values of the choices? (Assume r = 3.5% (annual))

Problem 4: (a)  If you will be making equal deposits into a retirement account for 10 years (with each payment at the end of the year), how much must you deposit each year if the account earns 8% compounded annuallyand you wish the account to grow to $3,000,000 after 40 years (in time 40)?  

(b)  How does your answer to part (a) change if the account pays interest compounded monthlyat an annual rate of 8%? Note: use monthly compounding for all calculations.

Problem 5: (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die).  If you will receive $42,000 per year at the end of each year starting 40 years from now (i.e., the first payment is in time 40), what is the present value of your retirement plan if the discount rate is 5.5%?

(b) How does your answer to part (a) change if you will receive $3,500 per month every month forever (in perpetuity) starting 40 years from today (the first payment is in time period 480) and you compound monthly?