Question

- What is the price of a bond paying a 6% semi-annual coupon bond if the yield on the bond is 7.5% and the bond has 3 years to maturity? Assume the face value of the bond is $1000.

Answer #1

We can use the following Yield to Maturity formula to calculate the Price of the bond. | |||||||||

Yield to Maturity = {C+[(F-P)/n]} / {(F+P)/2} | |||||||||

Yield to Maturity = 7.5% | |||||||||

C = semi annual coupon payment = Face value of bond x Semi annual coupon rate = $1000 x 3% = $30 | |||||||||

F = Face value of bond = $1000 | |||||||||

P = Price of Bond = ? | |||||||||

n = semi annual periods to maturity = 3 years x 2 = 6 | |||||||||

0.075 = {30+[(1000-P)/6]} / {(1000+P)/2} | |||||||||

0.075 = {30+166.67 - 0.1667P} / {500 + 0.5P} | |||||||||

37.5 + 0.0375P = 196.67 - 0.1667P | |||||||||

0.0204167P = 159.1667 | |||||||||

P = 779.59 | |||||||||

Price of bond = $779.59 |
|||||||||

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