Question

1.a. How much would you pay for a 10-year bond with a face value of $1,000 and a coupon rate of 8% if you wanted a 5% yield to maturity?

b. Find the rate of return for this bond if you plan to sell it after four years for $1,259.34.

Answer 1

Number of periods to maturity = n = 10 years

Yield to Maturity = r = 5%

Annual Coupon Payment P = 8%*1000 = $80

Face Value FV = $1000

Hence, PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= P[1 - (1+r)-n]/r + FV/(1+r)n = 80(1 - 1.05-1)/0.05 + 1000*.6139

=80*7.72173+1000*.6139

= $617.73+613.9 = $1231.6

b) Find the rate of return for this bond if you plan to sell it after four years for $1,259.34.

after 4 years value of bond

Number of periods to maturity = n = 4 years

Yield to Maturity = r = 5%

Annual Coupon Payment P = 8%*1000 = $80

Face Value FV = $1000

Hence, PV = P/(1+r) + P/(1+r)2 + .... + P/(1+r)n + FV/(1+r)n

= 283.6+822.70 = $1106.30

sell it = $1,259.34.

return =$1,259.34. - 1106.30 = 153.04

= 153.04/1000*100 = 15.304% rate of return