Question

A $1000 bond redeemable at $1050 on December 1, 2016, pays interest at j2 = 6.5%. The bond is bought on June 1, 2014 to yield j2 = 5.5% to maturity. (a) Determine the purchase price of the bond. (b) Construct the complete bond schedule.

Answer 1

a) As we know the YTM and coupon rate we can find out the purchase price of the bond as below. As the time is 2.5 years lets convert the rates to semi annually. Then,

Coupon Rate(C) = 3.25%

YTM = 2.75%

Face value(F) =1050

Time = 5 years

Putting this on the formula of YTM to calculate the purchase price (P) =

YTM = [C + ({F- P} /n)] / ({F+P}/ 2)

0.0275 = [32.5 + ({ 1050- P} /5) / ({ 1050 + P} / 2)

28.875+ 0.0275P = 63 + (2100-2P/5)

144.375 + 0.1375P = 325 + 2100- 2P

2.1375 P = 2280.625

P = 1066.9 = 1067

The price of the bond is $1067