Financial Markets and Institutions Ch. 2 HW

The current one-year T-bill rate is .50 percent and the expected one-year rate 12 months from now is 1.20 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security?

Current rate = .85% Calculations: (1.0050)(1.0120) = (1+R2)^2 1.01706 = (1+R2)^2 1.00849 = (1+R2) .00849 = R2 .00849 = .85%

Suppose we observe the following rates: 1R1 = 6.7%, 1R2 = 7.9%. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(2r1)?

Expected one-year interest rate = 9.11% Calculations: 1 + 1R2 = [(1+1R1)(1+E2R1)]^(1/2) 1+.079 = [(1+.067)(1+E2R1)]^(1/2) 1.079^2 = 1.067(1+E2R1) 1.1642 = 1.067(1+E2R1) 1.1642 / 1.067 = 1.0911 1.0911 - 1 = E2R1 = 9.11%

Based on economists' forecasts and analysis, one-year T-bill rates and liquidity premiums for the next four years are expected to be as follows: 1R1= .36% E(2r1)= .75% | L2= 0.08% E(3r1)= .85% | L3= 0.12% E(4r1)= 1.15% | L4= 0.13% Identify the four annual rates.

Year 1 = .36% Year 2 = .59 Year 3 = .72 Year 4 = .86 Calculations: Year 2 = [(1.0036)(1.0075 + .0008)]^(1/2) - 1 = .0059 Year 3 = [(1.0036)(1.0075 + .0008)(1.0085 + .0012)]^(1/3) - 1 = .0072 Year 4 = [(1.0036)(1.0075 + .0008)(1.0085 + .0012)(1.0115 + .0013)]^(1/4) - 1 = .0072

On March 11, 20XX, the existing or current (spot) one-year, two-year, three-year, and four-year zero-coupon Treasury security rates were as follows: 1R1 = 1.98%, 1R2 = 2.50%, 1R3 = 2.74%, 1R4 = 2.85% Using the unbiased expectations theory, calculate the one-year forward rates on zero-coupon Treasury bonds for years two, three, and four as of March 11, 20XX.

Year 2 = 3.02% Year 3 = 3.22 Year 4 = Calculations: Year 2 = [(1+.0250)^2 / (1+.0198)] -1 = .0302 Year 3 = [(1+.0274)^3 / (1+.0250)^2] -1 = .0322 Year 4 = [(1+.0285)^4 / (1+.0274)^3 ] -1 = .0318

Calculate the present value of $4,000 received five years from today if your investments pay a. 6 percent compounded annually b. 8 percent compounded annually c. 10 percent compounded annually d. 10 percent compounded semiannually e. 10 percent compounded quarterly

a. $2989.03 b. 2722.33 c. 2486.68 d. 2455.65 e. 2441.08 Calculations (using BAII Plus calculator): a. N= 5, I/Y= 6, FV= 4000, CPT PV b. N= 5, I/Y= 8, FV= 4000, CPT PV c. N= 5, I/Y= 10, FV= 4000, CPT PV d. N= (5*2), I/Y= (10/2), FV= 4000, CPT PV e. N= (5*4), I/Y= (10/4), FV= 4000, CPT PV

Calculate the present value of the following annuity streams: a. $7,000 received each year for 6 years on the last day of each year if your investments pay 6 percent compounded annually. b. $7,000 received each quarter for 6 years on the last day of each quarter if your investments pay 6 percent compounded quarterly. c. $7,000 received each year for 6 years on the first day of each year if your investments pay 6 percent compounded annually. d. $7,000 received each quarter for 6 years on the first day of each quarter if your investments pay 6 percent compounded quarterly.

a. $34421.27 b. 140212.84 c. 36486.55 d. 142316.03 Calculations: a. PV = $7,000 {[1 − (1/(1 + 0.06)^6)]/0.06} = $7,000 (4.917324) = $34,421.27 b. PV = $7,000 {[1 − (1/(1 + 0.015)^24)]/0.015} = $7,000 (20.030405) = $140,212.84 c. PV = $7,000 {[1 − (1/(1 + 0.06)^6)]/0.06}(1 + .06) = $7,000 (4.917324)(1 + 0.06) = $36,486.55 d. PV = $7,000 {[1 − (1/(1 + 0.015)^24)]/0.015}(1 + 0.015) = $7,000 (20.030405)(1 + 0.015) = $142,316.03

What are the monthly payments (principal and interest) on a 15-year home mortgage for an $230,000 loan when interest rates are fixed at 8 percent?

$2197.99 Calculations: N=(15*12) I/Y=(8/12) PV=-230,000, CPT PMT

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 = 0.5%, E(2r 1) = 1.5%, E(3r1) = 7.9%, E(4r1) = 8.25% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year maturity Treasury securities.

1 year = .50% 2 years = .99 3 years = 3.25 4 years = 4.48 Calculations: 1R2 = [(1+.005)(1+.015)]^(1/2) - 1 = .00998 1R3 = [(1+.005)(1+.015)(1+.079)]^(1/3) - 1 = .0325 1R4 = [(1+.005)(1+.015)(1+.079)(1+.0825)]^(1/4) - 1 = .04476

If an ounce of gold, valued at $740, increases at a rate of 7.9 percent per year, how long will it take to be valued at $1,000?

3.96 years Calculations: I/Y=7.9, PV=-740, FV=1000, CPT N

Calculate the future value in four years of $7,000 received today if your investments pay a. 6 percent compounded annually b. 8 percent compounded annually c. 10 percent compounded annually d. 10 percent compounded semiannually e. 10 percent compounded quarterly

a. $8837.34 b. 9523.42 c. 10248.70 d. 10342.19 e. 10391.54 Calculations (using BAII Plus calculator): a. N= 4, I/Y= 6, PV= -7000, CPT FV b. N= 4, I/Y= 8, PV= -7000, CPT FV c. N= 4, I/Y= 10, PV= -7000, CPT FV d. N= (4*2), I/Y= (10/2), PV= -7000, CPT FV e. N= (4*4), I/Y= (10/4), PV= -7000, CPT FV