Oil well supply offers 7.5 percent coupon bonds with semiannual payments and a yield to maturity of 7.68 percent. the bonds mature in 6 years. what is the market price per bond if the face value is $1,000?
a. $989.70
b. $991.47
c. $996.48
d. $1,002.60
e. $1,013.48

The answer is option (B), Market price=$991.47

Explanation:

The market price of a bond can be expressed as;

Market price=(Semi-annual coupon×((1-(1/1+r)^i)/r  + face value/(1+r)^i

where;

i-maturity period, period=(2×6)=12

r-nominal yield to maturity rate=7.68/2=3.84%

Semi-annual  coupon rate=7.5/2=3.75%

face value=$1,000

Semi- annual coupon=(3.75/100)×1,000=$37.50

replacing;

Market price=Semi-annual coupon×((1-(1/1+r)^i)/r  + face value/(1+r)^i

Market price=37.50×((1-(1/1+0.0384)^12)/0.0384 + 1,000/(1+0.0384)^12

Market price=(37.50×(1-0.64)/0.0384)+636.24

Market price=355.23+636.24

Market price=$991.47

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