A security with a five-year term costs $7500 and returns a single payment of $10,000 at maturity.

B. A security with a term of three months costs $49,000. It returns a single payment of $50,000 at maturity.

C. A security costs $8000. It returns a payment of $3000 after one year, a payment of $5,000 after three years, and a (final) payment of $2000 after five years.

D. A principal-and-interest security with a term of twelve years costs $102,000. It has a face value of $100,000 and a coupon rate of 7.5 percent.

E. An annuity costs $350,000. It returns a payment of $25,000 at the end of each of the next twenty years.

F. A security with a term of 8 years costs $100,000. It returns a payment at the end of every second year after it is issued. The first payment is $80,000. Each subsequent payment is half as large as the preceding payment.

2. Calculating return rates

Calculate the discount ratio, return ratio, annual return ratio and annual rate of return (interest rate) for each of the following securities:

A. The security from Question 1-A.

B. A security that has a twenty-year term, costs $350,000 and returns a single payment of $500,000 at maturity.

C. A security that has a two-year term, costs $9000, and returns a single payment of $10,000 at maturity.

D. A security that has a one-year term, costs $9000, and returns a single payment of $10,000 at maturity.

E. The security from Question 1-B.

F. A single-payment security that costs $10,000 and returns $11,500 after 16 months.

3.Interest rates and growth rates

Calculate the annual growth rate of each of the following items:

Hint: In each case, calculate the time interval between the two values, measured in years, and use it as the term.

A.The population of a small country. It was 35 million in 1995 and 70 million in 2015.

B.The height of a redwood tree. It was ten feet tall in 1960 and 100 feet tall in 2010.

C.A small countrys national debt, valued in U.S. dollars. It was $300 billion in 2000 and $450 billion in 2010.

D.The price level of a country suffering from very high inflation. Its price index was 155.8 in July 2013 and 1246.4 in January 2015.

E.The size of an endangered wetland. It was 250,000 acres in 2012 and 175,000 acres in 2015.

F.The price of a euro, in dollars. It was $1.36 in June 2014 and it is $1.12 in March 2015.

Part B-2

4. Calculate the market prices of the following single-payment bonds:

A. A bond with a five-year term that returns a payment of $20,000 and is issued at a time when the market interest rate is 8.2 percent.

B. A bond with a ten-year term that returns a payment of $75,000 and is issued when the market interest rate is 2.3 percent.

C. A bond with a term of one year that returns a payment of $100,000 and is issued when the market interest rate is 5.0 percent.

D. A six-month Treasury bill that returns a payment of $10,000 and is issued when the market interest rate is 4.1 percent.

E. A bond with a term of 18 months that returns a payment of $50,000 and is issued when the market interest rate is 6.9 percent.

5. Calculate the market prices of the following annuities:

A. An annuity with a 12-year term that returns annual payments of $10,000; at the time it is issued, the market interest rate is 13.5 percent.

B. An annuity that returns annual payments of $1000 over five years; it is issued when the market interest rate is 8.2 percent.

6. A principal and interest bond with a term of five years has a face value of $20,000 and a coupon interest rate of 5 percent. At the date it is issued, the market interest rate is 8.2 percent.

A. What is the market price of this bond?

B. How is the price of this bond related to the prices of the bonds in Questions 4-A and 5-B? How do you account for this relationship? Explain your answer carefully.

7. Calculate the market prices of the following multiple-payment bonds:

A. The bond from Question 1.C of this assignment, which returned a payment of $3000 after one year, a payment of $5000 after three years, and a (final) payment of $2000 after five years. The market interest rate is 8.55 percent.

B. 1. A bond that returns a payment of $20,000 after five years and a payment of $75,000 after ten years. The market interest rate is 2.3 percent.

2. Why isnt the price of this bond equal to the sum of the prices of the bonds from Questions 4.A and 4.B? Is it higher, or lower? Why? Explain carefully.

8. A P&I bond with a term of eight years has a face value of $10,000 and returns annual interest payments of $350.

A. What is the coupon interest rate on this bond?

Note: Answer Part B before doing Part C.

B. Suppose the market interest rate at the time the bond is issued is 4.5 percent.

1. Will this bond be sold at a discount or a premium? How do you know?

2. Suppose the issuer of this bond wants it to sell in the market at par.

Would he have to increase or decrease the annual interest payments? By how much? (Be specific.)

C. Calculate the market price of this bond if the market interest rate is 4.5 percent. What is the value of the discount or premium at which it sells?

9. The Indianapolis Colts turn to the free agent market to try to replace a wide receiver who has refused to report to training camp. They find an attractive free agent and sign him to long-term (12-year) contract. The contract has the following provisions:

The player receives a signing bonus of $1,500,000 immediately.

He receives a salary payment of $3,000,000 at the end of each of the next five years.

He receives deferred payments of $500,000 per year for seven years, beginning at the end of the sixth year after he signs the contract.

During a press conference at which the signing is announced, the players agent describes the agreement as a twenty million dollar contract.

A. In what sense is the agents description correct? Explain.

B. 1. In what sense is the agents description incorrect? Explain.

Hint: It may be helpful to answer the next question before you try to answer this one.

Assume, here and below, that the market interest rate is 6 percent. How much would it cost the Colts, in money paid up front, to arrange for a bank to make the various payments, including the signing bonus, required by the contract?

Hints: What is the market price of a bond that returns these payments? What is the present value of a payment received immediately? How can you adapt the annuity formula to cover the case of equal annual payments that begin several years in the future?

3. How much would each of the five annual salary payments have to be increased, leaving the other payments unchanged, so that the present value of the contract would really be $20 million?