1. Your uncle died last year and left you money in his will. You are to receive $400,000 in five years (time 5) and $600,000 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 7% and you compound annually?

(b) If you invest the money when you receive it, how much will it grow to 30 years from today (i.e., in time 30) if you earn 7% each year?

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

I. Pays $90,000 today (in time 0)

II. Buy under a "no payments for three years" program by agreeing to pay $110,000 three years from today (in time 3).

III. Make 60 monthly payments over 5 years of $1,750 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?

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

I. Early retirement (Age 62 exactly) $800 per month for life

II. Regular retirement (Age 66 years, 2 months) $1,000 per month for life

III. Delayed retirement (Age 70 exactly) $1,240 per month for life

If her expected life expectancy is 80 years old (exactly), what are the present values of the choices? (Assume r = 6% (annual))

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 5% compounded annually and you wish the account to grow to $1,000,000 after 30 years (in time 30)?

(b) How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 5%? Note: use monthly compounding for all calculations.

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 $48,000 per year at the end of each year starting 30 years from now (i.e., the first payment is in time 30), what is the present value of your retirement plan if the discount rate is 5%?

(b) How does your answer to part (a) change if you receive $4,000 per month every month forever (in perpetuity) starting 30 years from today (in monthly time period 360) and you compound monthly?