5. What is the price today of a $200,000 cash flow in 5 years if the discount rate is 2.5%

6. What is the price today of $200,000 to be received in 6 years if the rate of discount is 2.5%? Compare to #5.

7. What is the price today of $200,000 to be received in 5 years if the rate of discount is 3%? Compare to #5.

10. An asset promises to pay $50,000 in five years and $100,000 in ten years. What is its price if the 5-year rate of discount is 10% and the 10-year rate of discount is 5%?

9. a) What must be the interest rate in order for an investment of $1,000 to produce proceeds of $2,000 in 20 years?

b) If a cash flow of $2,000 in 20 years has a price today of $1,000, what must be the discount rate (i.e., the implied rate)?

11. An asset promises to pay $1,000 in each of the next two years.

a) What is its present value assuming the one-year rate of discount is 1.5% and the two-year is 2.2%?

b) What is its present value assuming both discount rates are 1.85%?

12. An asset promises to pay $60 in each of the next three years. Assume the rate of discount is 5% for each of the years.

a) Calculate its price the long way; i.e., just as you have been doing for #10 and #11, by discounting each future cash flow and summing.

b) Calculate its price using the annuity formula.

13. For the annuity in #12, what happens to it price if the rate of discount increase to 6%?

14. For the annuity in #12, what happens to it price if:

15. What are the proceeds of $1,000,000 deposited in a bank on July 10 for 1 month at 1.5%? Take care to apply money market rules and use the proper day count.

16. What is the present value as of July 11 of $1MM to be paid January 11 2020 at a (discount) rate of 2%? (Same instructions as in #15.)

17. An asset promises to pay the following:

• $60 each year for the next ten years: and
• $1,000 in ten years

Assume all the cash flows are discounted by 6%. Use the annuity formula to get the price of the first part. Use the standard discounting formula to get the price of the second part. Add them together. This is a bond! It is described as paying a coupon rate of 60/1,000 = 6% (a coupon of 60), with a face value of 1,000 and a maturity of ten years. Its yield-to-maturity is 6%.

18. a) The U.S. Treasury has issued an IOU to pay $100,000 in 1 year (a 1-year Treasury bill). If investors discount this cash flow by 4%, what is its price?

b) A corporation issues the same IOU. Investors add a risk premium of 80 basis points (0.80%). What is its price?

c) Suppose there is a 90% probability that the company will make good on its promised cash flow. There is a 10% chance that it will not (i.e., default), in which case the IOU investor receives $92,500. Can you calculate the expected proceeds the probability-weighted sum of the two possible outcomes? Would the investor ever receive the expected amount? If not, how may it be termed expected?!!!

d) The U.S. Treasury has issued another IOU to pay $250,000 in 2 years. The market prices it at $230,695. The above corporation issues the same IOU and the market prices it at $226,325. What is the implied risk premium?