Level and Structure of Interest Rates
Please put all of your answers and computations on a separate sheet(s).
1. Suppose that the demand and supply of loanable funds can be represented as follows. (Note the interest rate is in absolute terms; not decimals)
q = 30 - 1.5i
q = -2 + 2i
where the q's are quantities of loanable funds and i is the interest rate.
a. What is the initial interest rate and quantity of loanable funds?
b. Suppose the demand for loanable funds becomes q = 40 - 1.5i. What is the new interest rate and quantity of loanable funds assuming the supply function remains the same? What could cause such a change in the demand for loanable funds?
c. Suppose the demand for loanable funds becomes q = 20 - 1.5i . What is the new interest rate and quantity of loanable funds assuming the supply function remains the same? What could cause such a change in the demand for loanable funds
d. Suppose the supply of loanable funds becomes q = 2i and the demand is q = 3 - 1.5i. What is the new interest rate and quantity of loanable funds? What could cause such a change in the supply for loanable funds?
2. Suppose you find the following rates on Yahoo Finance:
1R1 = 12%, 1R2 = 16% and E(2r1) = 12%. If the liquidity premium theory of the term is applicable, what is the liquidity premium for year 2?
3. What are the monthly payments on a 30 year home mortgage for a $300,000loan when the interests are fixed at 6 percent?
4. Suppose that the current one-year spot rate and one-year expected rate on a T-bill over the next four years are as follows:
1R1 = 5%, E(2r1) = 8%, E(3r1) = 9.5%, E(4r1) = 11%, E(5r1) = 9%
Using the unbiased expectations approach, construct the term structure of interest rates. Plot the yield curve.
5. Yahoo Finance reported spot rates of 6 percent, 7.35 percent, 7.65 percent, and 8.00 percent for three-year, four-year, five-year, and six-year T-bills, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6 (i.e., what are 4f1, 5f1, and 6f1)?
6. If an ounce of gold, valued at $1,500, increases at a rate of 8.5 percent per year, how long will it take to be valued at $3000?
7. Calculate the present value of the following annuity streams
a. $8000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.
b. $8,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded semi-annually.
c. $8,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly.
8. A particular security's equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. The security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security's default risk premium.
9. Using Fisher's interest rate equation, show that the real rate is r = (i -ρ) / (1 + ρ).