Chp 2 Determinants of Interest Rates

YIELD CURVE FOR ZERO COUPON BONDS RATED AA Assume that there are no liquidity premiums. To the nearest basis point, what is the expected interest rate on a four-year maturity AA zero coupon bond purchased six years from today?

10.41 percent ((1.0947^10/1.0885^6))^(1/4) -1

You go to the Wall Street Journal and notice that yields on almost all corporate and Treasury bonds have decreased. The yield decreases may be explained by which one of the following?

A decrease in U.S. inflationary expectations

Of the following, the most likely effect of an increase in income tax rates would be to

All of the options. decrease the savings rate. decrease the supply of loanable funds. increase interest rates.

One-year T-bills currently earn 0.43 percent. You expect that one year from now, one-year T-bill rates will increase to 0.48 percent. If the unbiased expectations theory is correct, what should the current rate be on two-year Treasury securities?

Current rate on two-year Treasury securities 0.46% 1R2 = [(1 + 0.0043)(1 + 0.0048)]^1/2 − 1 = .46%

An annuity and an annuity due with the same number of payments have the same future value if r = 10%. Which one has the higher payment?

The annuity has the higher payment.

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 = .42% E(2r1) = .78% L2 = 0.07% E(3r1) = .88% L3 = 0.11% E(4r1) = 1.18% L4 = 0.12% Identify the four annual rates.

Annual Rates Year 1 0.42% Year 2 0.63% Year 3 0.75% Year 4 0.89% 1R1 = 0.42% 1R2 = [(1 + 0.0042)(1 + 0.0078 + 0.0007)]^1/2 − 1 = 0.63% 1R3 = [(1 + 0.0042)(1 + 0.0078 + 0.0007)(1 + 0.0088 + 0.0011)]^1/3 − 1 = 0.75% 1R4 = [(1 + 0.0042)(1 + 0.0078 + 0.0007)(1 + 0.0088 + 0.0011)(1 + 0.0118 + 0.0012)]^1/4 − 1 = 0.89%

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 = 0.4%, E(2r 1) = 1.4%, E(3r1) = 1.9%, E(4r1) = 2.25% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year maturity Treasury securities.

Current (Long-Term) Rates One-year 0.400% Two-year 0.899% Three-year 1.231% Four-year 1.485% 1R1 = 0.400% 1R2 = [(1 + 0.004)(1 + 0.014)]^1/2 − 1 = 0.899% 1R3 = [(1 + 0.004)(1 + 0.014)(1 + 0.019)]^1/3 − 1 = 1.231% 1R4 = [(1 + .0.004)(1 + 0.014)(1 + 0.019)(1 + 0.0225)]^1/4 − 1 = 1.485%

You can save $6,000 per year for the next two years in an account earning 6 percent per year. How much will you have at the end of the second year if you make the first deposit today?

Future value $ 13,101.60 FV = $6,000 {[(1 + 0.06)^2 − 1]/0.06}(1 + .06) = $13,101.60 or using a financial calculator, set the calculator to Begin mode and then enter N = 2, I = 6, PV = 0, PMT = −6,000, then compute FV = $13,101.60.

Which of the following would normally be expected to result in an increase in the supply of funds, all else equal? I. The perceived riskiness of all investments decreases. II. Expected inflation increases. III. Current income and wealth levels increase. IV. Near term spending needs of households increase as energy costs rise.

I and III only

Classify each of the following in terms of their effect on interest rates (increase or decrease): I. Covenants on borrowing become more restrictive. II. The Federal Reserve increases the money supply. III. Total household wealth increases.

I decreases, II decreases, III decreases

An investor wants to be able to buy 4 percent more goods and services in the future in order to induce her to invest today. During the investment period prices are expected to rise by 2 percent. Which statement(s) below is/are true? I. 4 percent is the desired real risk-free interest rate. II. 6 percent is the approximate nominal rate of interest required. III. 2 percent is the expected inflation rate over the period.

I, II, and III are true

What are the monthly payments (principal and interest) on a 15-year home mortgage for an $240,000 loan when interest rates are fixed at 8 percent?

Monthly payments $ 2,293.57 PV = $240,000 = PMT {[1 − (1/(1 + 0.08/12)^15x12)]/(0.08/12)} = $2,293.57 or using a financial calculator, N = 15 × 12 = 180, I = 8 ÷ 12 = 0.66667, PV = −240,000, FV = 0, then compute PMT = $2,293.57.

Classify each of the following in terms of their effect on interest rates (increase or decrease): I. Perceived risk of financial securities increases. II. Near term spending needs decrease. III. Future profitability of real investments increases.

None of the options

If you note the following yield curve in The Wall Street Journal, what is the one-year forward rate for the period beginning one year from today, 2f1 according to the unbiased expectations theory? Maturity Yield One day 2.23% One year 2.55 Two years 2.79 Three years 2.90

One-year forward rate 3.03% (1 + 1R2)2 = (1 + 1R1)(1 + 2f1) 1R2 = 0.0279 = [(1 + 0.0255)(1 + 2f1)]1/2 - 1 ⇒ [(1.0279)2/(1.0255)] - 1 = 2f1 = 3.03%

Calculate the future value in five years of $4,000 received today if your investments pay. Future Value a. 7 percent compounded annually $ 5,610.21 b. 9 percent compounded annually 6,154.50 c. 11 percent compounded annually 6,740.23 d. 11 percent compounded semiannually 6,832.58 e. 11 percent compounded quarterly 6,881.71

a. FV = $4,000 (1 + 0.07)^5 = $4,000 (1.402552) = $5,610.21 b. FV = $4,000 (1 + 0.09)^5 = $4,000 (1.538624) = $6,154.50 c. FV = $4,000 (1 + 0.11)^5 = $4,000 (1.685058) = $6,740.23 d. FV = $4,000 (1 + 0.055)^10 = $4,000 (1.708144) = $6,832.58 e. FV = $4,000 (1 + 0.0275)^20 = $4,000 (1.720428) = $6,881.71

Calculate the future value of the following annuity streams: a. $5,000 received each year for 4 years on the last day of each year if your investments pay 5 percent compounded annually. Future value $ 21,550.63 b. $5,000 received each quarter for 4 years on the last day of each quarter if your investments pay 5 percent compounded quarterly. Future value $ 87,955.82 c. $5,000 received each year for 4 years on the first day of each year if your investments pay 5 percent compounded annually. Future value $ 22,628.16 d. $5,000 received each quarter for 4 years on the first day of each quarter if your investments pay 5 percent compounded quarterly. Future value $ 89,055.27

a. FV = $5,000 {[(1 + 0.05)^4 − 1]/0.05} = $5,000 (4.310125) = $21,550.63 b. FV = $5,000 {[(1 + 0.0125)^16 − 1]/0.0125} = $5,000 (17.591164) = $87,955.82 c. FV = $5,000 {[(1 + 0.05)^4 − 1]/0.05}(1 + 0.05) = $5,000 (4.310125)(1 + 0.05) = $22,628.16 d. FV = $5,000 {[(1 + 0.0125)^16 − 1]/0.0125}(1 + 0.0125) = $5,000 (17.591164)(1 + 0.0125) = $89,055.27

Calculate the present value of $6,000 received five years from today if your investments pay. Present Value a. 5 percent compounded annually $ 4,701.16 b. 7 percent compounded annually 4,277.92 c. 9 percent compounded annually 3,899.59 d. 9 percent compounded semiannually 3,863.57 e. 9 percent compounded quarterly 3,844.90

a. PV = $6,000/(1 + 0.05)^5 = $6,000 (0.783526) = $4,701.16 b. PV = $6,000/(1 + 0.07)^5 = $6,000 (0.712986) = $4,277.92 c. PV = $6,000/(1 + 0.09)^5 = $6,000 (0.649931) = $3,899.59 d. PV = $6,000/(1 + 0.045)^10 = $6,000 (0.643928) = $3,863.57 e. PV = $6,000/(1 + 0.0225)^20 = $6,000 (0.640816) = $3,844.90

According to the liquidity premium theory of interest rates,

long-term spot rates are higher than the average of current and expected future short-term rates.

Inflation causes the demand curve for loanable funds to shift to the _____ and causes the supply curve to shift to the _____.

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