Question

A government bond matures in 6 years, makes annual coupon payments of 5.5% and offers a yield of 3.5% annually compounded. Assume face value is $1,000. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) a. Suppose that one year later the bond still yields 3.5%. What return has the bondholder earned over the 12-month period?

Rate of Return %=

b. Now suppose that the bond yields 2.5% at the end of the year. What return did the bondholder earn in this case?

Rate of Return %+

Answer 1

a)

Value of Bond =

1- (1+r)" Coupon * Maturity Value + (1+r) r

Where r is the discounting rate of a compounding period i.e. 0.035

And n is the no of Compounding periods 6 years

Coupon 0.055

= 55*1-1/(1+0.035)^6/0.035+1,000/(1+0.035)^6

= 1106.57

Value of Bond after a year

Value of Bond =

1- (1+r)" Coupon * Maturity Value + (1+r) r

Where r is the discounting rate of a compounding period i.e. 0.035

And n is the no of Compounding periods 5 years

Coupon 0.055

= 55*1-1/(1+0.035)^5/0.035+1,000/(1+0.035)^5

= 1090.30

Return % = Coupon + Capital Gain / Purchase Price

= 55 + (1090.30 - 1106.57) / 1106.57

= 3.50%  

b)

Value of Bond after a year

Value of Bond =

1- (1+r)" Coupon * Maturity Value + (1+r) r

Where r is the discounting rate of a compounding period i.e. 0.025

And n is the no of Compounding periods 5 years

Coupon 0.055

= 55*1-1/(1+0.025)^5/0.025+1,000/(1+0.025)^5

= 1139.37

Return % = Coupon + Capital Gain / Purchase Price

= 55 + (1139.37 - 1106.57) / 1106.57

= 7.93%  

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