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%

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