A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to maturity on the bond is 10%, calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments.
A) $857.96
B) $949.24
C) $1057.54
D) $1000.00

Question

Quizplus · Accepted Answer

The bond has a face value of $1000 and a coupon rate of 8% which means that it pays $80 in interest per year. Since the coupon payments are made semi-annually, the amount of each coupon payment is $40 ($80/2). 
The bond maturity is three years which means that there will be six coupon payments in total. 
To calculate the price of the bond, we can use the formula for present value of a bond:
PV = (C/(1+r/2)^1) + (C/(1+r/2)^2) + ... + (C/(1+r/2)^6) + (FV/(1+r/2)^6)
where C = semi-annual coupon payment, FV = face value, and r = yield to maturity.

Plugging in the numbers, we get: 
PV = (40/(1+0.10/2)^1) + (40/(1+0.10/2)^2) + ... + (40/(1+0.10/2)^6) + (1000/(1+0.10/2)^6)
PV = $949.24

Therefore, the price of the bond is $949.24, which is closest to answer choice B.

A Three-Year Bond Has 8