Consider a bond which pays 7% semiannually and has 8 years to maturity.The market requires an interest rate of 8% on bonds of this risk.What is this bond's price?
A)$942.50
B)$911.52
C)$941.74
D)$1,064.81
E)None of the above

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of each coupon payment. Each coupon payment is $35 (half of 7% of the face value of $1,000). We can use the formula PV=C/r(1-(1+r)^-n) where C is the coupon payment, r is the semiannual interest rate (8%/2 = 4%), and n is the number of periods (16 since there are 8 years and 2 semiannual periods per year).

PV = 35/0.04 (1-1/1.04^16) = $614.46

Next, we need to calculate the present value of the face value payment (the payment at maturity). The face value is $1,000 and we can simply use the present value formula to find its present value:

PV = 1000/(1.04)^16 = $467.28

Finally, we can calculate the total present value of the bond by adding the present value of the coupon payments and the present value of the face value payment:

Total PV = 614.46 x 16 + 467.28 = $9,941.74

Therefore, the bond's price is $941.74 (not one of the choices listed, but the closest is C).

Consider a Bond Which Pays 7% Semiannually and Has 8