ECO 3223 Homework Assignment #1, Spring 2015

Instructions: Answer each of the following questions, showing your work where appropriate.Due: Tuesday, February 10th at the beginning of class1. In 2012, there were 314 million people living in the United States.a. If the U.S. population grows at a constant rate of 3% per year, what will the population be in2022?b. If the population grows at a constant rate of 3% per year, what would the population havebeen in 2006?c. Suppose that the U.S. population has been growing at 3% per year, but at the beginning of2015, the growth rate falls to 1.5% per year and remains there until 2022. What will thepopulation be in 2022?d. At what rate would the population need to grow between 2012 and 2022 in order for thereto be 400 million people living in the United States at the beginning of 2022?2. Suppose that you own a zero coupon bond that will mature in 4 years. The face value of thebond is $10,000.a. If the (nominal) interest rate is currently 5% and is expected to remain at 5% for the next 4years, what is the present value of your bond?b. Assuming that you are right about future interest rates, what will the bonds value be in 2years?c. If the (nominal) interest rate is currently 5%, but is expected to rise to 10% after 2 years(and remain at 10% after that), what is the present value of the bond?d. Assuming that you are right about future interest rates, what will the bonds value be in 2years?3. Consider a 5 year coupon bond with a 15% coupon rate and $1000 face value. Couponpayments are made once each year, at the end of the year.a. If the (nominal) interest rate is 8% at the time the bond is issued and is expected to remainat 8% for the next 5 years, what will be the present value of the bond at the time it isissued?b. If the (nominal) interest rate is 8% at the time the bond is issued, but is expected to fall to4% after 2 years (and remain there), what will be the present value of the bond at the timeit is issued?4. Suppose you win $10 million in the Florida State Lottery. You are given the choice betweenreceiving your winnings in $1 million increments paid every year (at the end of the year) for10 years or receiving 3 million immediately and the balance ($7 million) in 10 years.a. Which payment scheme should you take if the per-annum interest rate is 6%? Assume thatthe price of goods and services is not expected to rise significantly over the next 10 years.Why?b. Might you make a different choice if the interest rate were higher? Explain.5. Consider a newly issued 2 year coupon bond with a 5% coupon rate and a $10,000 facevalue. Coupon payments are made once each year, at the end of the year.a. What is the bonds (nominal) yield to maturity if it sells for $9900?b. At what price would a 2-year zero coupon bond with a $10,000 face value have to sell inorder to offer an equivalent yield to maturity?c. What is the coupon bonds (nominal) yield to maturity if it sells for $10,000?d. In that case, at what price would a 2-year zero coupon bond with a $10,000 face value haveto sell in order to offer an equivalent yield to maturity?6. Suppose that you purchase a 2 year coupon bond at the time it is issued for $1100. The facevalue of the bond is $1000, with annual coupon payments of $80.What is the bonds coupon rate?What is the bonds current yield?What is the bonds (nominal) yield to maturity?If you hold the bond for 1 year and sell it for $1035 (after collecting the first couponpayment), what is your holding period rate of return?7. Suppose that you purchase a zero coupon bond with a face value of $1000 at the time it isissued for $980.a. If the bond matures in 30 days, what is its yield to maturity (per year)?b. If the bond matures in 90 days, what is its yield to maturity (per year)?c. If the bond matures in 2 years, what is its yield to maturity (per year)?8. Consider a 2 year, zero coupon bond with a face value of $1000.If the bond sells for $940, what is its (nominal) yield to maturity?If the bond sells for $960, what is its (nominal) yield to maturity?If the bond sells for $980, what is its (nominal) yield to maturity?In general, how are bond prices and bond yields related, all else equal?9. Describe the difference between a bonds yield to maturity and its holding period rate ofreturn. Under what conditions would they be the same for a coupon bond?10. What is the difference between an annuity and a coupon bond? How much would youexpect to pay for a 20 year annuity that makes annual payments of $1000 if the interest rateis expected to average 3.5% over that period? How much would you expect to pay for a 20year, $10,000 (face value) bond that makes annual coupon payments of $1000 if the interestrate is expected to average 3.5% over that period?11. Suppose that you buy a 3 year, $10,000 (face value) coupon bond with a 7% coupon rate for$10,000 at the time it is issued. Coupon payments are made once each year, at the end ofthe year.a. What is the (nominal) yield to maturity offered by the bond?b. At the end of 1 year (after collecting the first coupon payment), you decide to sell the bond.If the nominal interest rate is 7% at the end of one year (and expected to remain there),what price will the bond sell for? What will be your holding period rate of return?c. If, instead, the nominal interest rate is 10% at the end of one year, what price will the bondsell for? What will be your holding period rate of return in that case?d. Suppose, instead, that you hold the bond for 2 years (and collect 2 coupon payments)before you decide to sell it. If the nominal interest rate is 10% at the end of 2 years, whatprice will the bond sell for? What will be your holding period rate of return?12. Suppose you take out a $12,000 fixed payment loan to purchase a car. The loan is to berepaid in monthly installments over a term of 3 years. If your loan is obtained at an annualnominal interest rate of 6.5%, and interest is compounded monthly, how much will yourmonthly payments be?13. Describe the difference between the nominal interest rate offered on a loan and the expost real interest rate? In general, how is the ex-post real interest rate related to thenominal interest rate?14. Suppose you buy a 3 year, zero coupon bond with a face value of $1000 at the time it isissued.a. If you buy the bond for $920, what is its nominal yield to maturity?b. What is the bonds ex-ante real yield to maturity, if the inflation rate is expected to average2% per year over the next 3 years?c. Suppose that after 2 years, you sell the bond for $990. What nominal holding period rate ofreturn have you earned?d. What was your real holding period rate of return if the inflation rate was 2% over the twoyears that you held the bond?