A bond with a face value of $1,000 has 10 years until maturity, carries a coupon rate of 7.3%, and sells for $1,170. Interest is paid annually. a. If the bond has a yield to maturity of 10.7% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your anser to nearest whole number.)b. What will be the annual rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)c. Now assume that interest is paid semiannually. What will be the annual rate of return on the bond?Slightly greater than your part b answerSlightly less than your part b answerd. If the inflation rate during the year is 3%, what is the annual real rate of return on the bond? (Assume annual interest payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

a. Price 1 year later = $810

b. Annual rate of return on the bond = -24.53%

c. Since -24.79% is lower than -24.53% obtained part b, this implies that annual rate of return is slightly less than our part b answer.

d. Annual real rate of return on the bond = -26.73%

Explanation:

a. If the bond has a yield to maturity of 10.7% 1 year from now, what will its price be at that time? (Do not round intermediate calculations. Round your answer to nearest whole number.)

This can be calculated as follows:

Price 1 year later = Coupon rate * Par value / Yield to maturity * (1 - 1 / (100% + Yield to maturity)^Years to maturity) + Par value / (100% + Yield to maturity)^Years to maturity = 7.3% * 1000 / 10.7% * (1 - 1 / (100% + 10.7%)^9) + 1000 / (100% + 10.7%)^9 = $810

b. What will be the annual rate of return on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

This can be calculated as follows:

Annual rate of return on the bond = (Price 1 year later + Coupon rate * Par value) / Price now - 1 = (810 + 7.3% * 1000) / 1170 - 1 = -24.53%

c. Now assume that interest is paid semiannually. What will be the annual rate of return on the bond?Slightly greater than your part b answer Slightly less than your part b answer

This can be determined as follows:

Price 1 year later = (Coupon rate / 2) * Par value / (Yield to maturity / 2) * (1 - 1 / (100% + (Yield to maturity / 2))^(Years to maturity * 2)) + Par value / (100% + (Yield to maturity / 2))^(Years to maturity * 2) = (7.3% / 2) * 1000 / (10.7% / 2) * (1 - 1 / (100% + (10.7% / 2))^(9 * 2)) + 1000 / (100% + (10.7% / 2))^(9 * 2) = $807

Annual rate of return on the bond = (Price 1 year later + Coupon rate * Par value) / Price now - 1 = (807 + (7.3% / 2) * 1000) / 1170 - 1 = -24.79%

Since -24.79% is lower than -24.53% obtained part b, this implies that annual rate of return is slightly less than our part b answer.

d. If the inflation rate during the year is 3%, what is the annual real rate of return on the bond? (Assume annual interest payments.) (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

This can be calculated as follows:

Annual real rate of return on the bond = (1 + nominal return) / (1 + inflation)-1 = (1 - 24.53%) / (1 +3 %) - 1 = -26.73%

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