2. Your uncle died last year and left you money in his will. You are to receive $300,000 five years from today (i.e., in time 5).

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

(b) If you invest the money when you receive it in time 5, how much will it grow to 30 years from today (i.e., in time 30) if you earn 5% each year?

3. Your neighbor is buying a new recreational vehicle (RV). He has the following options to finance the RV:

I. Pays $67,500 today (in time 0)

II. Buy under a delayed payment program requiring payments of $10,000 in time 1, $12,500 in time 2, $15,000 in time 3 and $17,500 in time 4 and $20,000 in time 5.

III. Make 84 monthly payments of $920 payable at the beginning of each month (in other words, the first payment is at time 0).

(a) If the interest rate is 6.25% annually, calculate the present value of each option.

(b) What is the interest rate where Option I and Option II have the same present value?

4. (a) If you will be making equal deposits into a retirement account for the next 20 years (with each payment at the end of the year 1 through 20), how much must you deposit each year if the account earns 4.8% compounded annually and you wish the account to grow to $1,000,000 40 years from today (in time 40)?

(b) How does your answer change if the account pays interest compounded monthly at an annual rate of 4.8%? 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 $36,000 per year at the end of each year starting 30 years from now, what is the present value of your retirement plan if the discount rate is 5.75%?

(b) How does your answer change if you receive $3,000 per month every month starting 30 years from today (in monthly time period 360) using an annual rate of 5.75% (adjusted to make it monthly)?