04 Jun Question Instructions: Answer each of the following questions, showing your work where appropriate. Due: Tuesday, February 10th at the
Question
Instructions: Answer each of the following questions, showing your work where appropriate.
Due: Tuesday, February 10th at the beginning of class
1. 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 in
2022?
b. If the population grows at a constant rate of 3% per year, what would the population have
been in 2006?
c. Suppose that the U.S. population has been growing at 3% per year, but at the beginning of
2015, the growth rate falls to 1.5% per year and remains there until 2022. What will the
population be in 2022?
d. At what rate would the population need to grow between 2012 and 2022 in order for there
to 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 the
bond is $10,000.
a. If the (nominal) interest rate is currently 5% and is expected to remain at 5% for the next 4
years, 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 2
years?
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 2
years?
3. Consider a 5 year coupon bond with a 15% coupon rate and $1000 face value. Coupon
payments 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 remain
at 8% for the next 5 years, what will be the present value of the bond at the time it is
issued?
b. If the (nominal) interest rate is 8% at the time the bond is issued, but is expected to fall to
4% after 2 years (and remain there), what will be the present value of the bond at the time
it is issued?
4. Suppose you win $10 million in the Florida State Lottery. You are given the choice between
receiving your winnings in $1 million increments paid every year (at the end of the year) for
10 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 that
the 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 face
value. 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 in
order 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 have
to 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 face
value 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?
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