Question

1a. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

₁R₁ = 0.3%, E(₂r ₁) = 1.3%, E(₃r₁) = 10.4%, E(₄r₁) = 10.75%

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. (Round your answers to 3 decimal places. (e.g., 32.161))

1b.The Wall Street Journal reports that the rate on four-year Treasury securities is 1.3 percent and the rate on five-year Treasury securities is 2.8 percent. According to the unbiased expectations hypotheses, what does the market expect the one-year Treasury rate to be four years from today, E(₅r₁)? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

1c.Assume the current interest rate on a one-year Treasury bond (₁R₁) is 1.69 percent, the current rate on a two-year Treasury bond (₁R₂) is 1.85 percent, and the current rate on a three-year Treasury bond (₁R₃) is 1.96 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year interest rate expected on T-bills during year 3 (E(₃r₁) or ₃f₁)? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

1d.Calculate the future value of the following annuity streams:

a. $8,000 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 quarterly.
c. $8,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.
d. $8,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.
  
(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

a. Future Value:

b. Future Value:

c. Future Value:

d. Future Value:

Answer 1

1a)

Current (long-term) rates for one-year maturity Treasury Security = 1R1 = 0.3%

Current (long-term) rates for two-year maturity Treasury Security

= ((1+1R1)*(1+2R1))^0.5-1

= (1.003*1.013)^0.5-1

= 0.007987 or 0.799%

Current (long-term) rates for three-year maturity Treasury Security

= ((1+1R1)*(1+2R1)*(1+3R1))^(1/3)-1

= (1.003*1.013*1.104)^(1/3)-1

= 0.0390261 or 3.903%

Current (long-term) rates for four-year maturity Treasury Security

= ((1+1R1)*(1+2R1)*(1+3R1)*(1+4R1))^(1/4)-1

= (1.003*1.013*1.104*1.1075)^(1/4)-1

= 0.0557371 or 5.574%

1b)

One-year Treasury rate to be four years from today, E(₅r₁)

E(₅r₁) = (1+5 year Treasury securities rate)^5/(1+ 4 year Treasury Securities rate)^4 - 1

=1.028^5/1.013^4-1

= 0.090254 or 9.03%

1c)

one-year interest rate expected on T-bills during year 3

(E(₃r₁) or ₃f₁) =(1+3 year Treasury securities rate)^3/(1+ 2 year Treasury Securities rate)^2 - 1

=1.0196^3/1.0185^2-1

=0.02180 or 2.18%

1d)

a)  Future value of $8,000 received each year for 5 years on the last day of each year if your investments pay 6 percent compounded annually.

=8000/0.06*(1.06^5-1)

=$45096.74

b) Future value of $8,000 received each quarter for 5 years on the last day of each quarter if your investments pay 6 percent compounded quarterly

Interest rate per quarter = 6%/4 = 1.5%

No of quarters = 5*4 =20

So, Future Value =8000/0.015*(1.015^20-1)

=$184989.34

c) Future value of $8,000 received each year for 5 years on the first day of each year if your investments pay 6 percent compounded annually.

= 8000/0.06*(1.06^5-1) * 1.06

=$47802.55

d) Future value of $8,000 received each quarter for 5 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

nterest rate per quarter = 6%/4 = 1.5%

No of quarters = 5*4 =20

So, Future Value =8000/0.015*(1.015^20-1)*1.015

=$187764.18