Consider the following $1,000 par value zero-coupon bonds:

Bond Years until Maturity Yield to Maturity

A 1 7.50%

B 2 8.50

C 3 9.00

D 4 9.50

a. According to the expectations hypothesis, what is the market's expectation of the one-year interest rate three years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. What are the expected values of next year's yields on bonds with maturities of (a) 1 year; (b) 2 years; (c) 3 years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. The market's expectation of the one-year interest rate three years from now is 11.01%

b. a The expected values of next year's yields on bonds with maturities of 1 year is 9.51%

b. b The expected values of next year's yields on bonds with maturities of 2 years is 9.76%

b. c The expected values of next year's yields on bonds with maturities of 3 years is 10.17%

Explanation:

According to expectations hypothesis, If market's expectation of 1-year rate three years from now is r, then:

(1 + 9%) ∧3 * (1 + r) ∧1 = (1 + 9.5%) ∧4

a. r = 11.01%

The market's expectation of the one-year interest rate three years from now is 11.01%

If the expected value of next year's yields on 1 year bonds is r, then:

(1 + 7.5%) ∧1 * (1 + r) ∧1 = (1 + 8.5%) ∧2

b. a r = 9.51%

If the expected value of next year's yields on 2 year bonds is r, then:

(1 + 7.5%) ∧1 * (1 + r) ∧2 = (1 + 9%) ∧3

b. b r = 9.76%

If the expected value of next year's yields on 3 year bonds is r, then:

(1 + 7.5%) ∧1 * (1 + r) ∧3 = (1 + 9.5%) ∧4

b. c r = 10.17%