What must be the price of a $10,000 bond with a 6.5% coupon rate, semiannual coupons, and two years to maturity if it has a yield to maturity of 8% APR?

Question

Quizplus · Accepted Answer

First, we need to calculate the semiannual coupon payment:
Coupon payment = (Coupon rate * Face value) / Number of coupon payments per year
Coupon payment = (0.065 * 10000) / 2 = $325

Next, we need to calculate the present value of each coupon payment using the yield to maturity:
PV of coupon payment = Coupon payment / (1 + YTM/2) ^ (number of years * number of coupon payments per year)
PV of coupon payment = 325 / (1 + 0.08/2)^(2*2) = $550.74

Then, we need to calculate the present value of the face value or principal using the yield to maturity:
PV of face value = Face value / (1 + YTM/2) ^ (number of years * number of coupon payments per year)
PV of face value = 10000 / (1 + 0.08/2)^(2*2) = $9052.01

Finally, we can add up the present values of the coupon payments and face value to get the bond price:
Bond price = PV of coupon payments + PV of face value
Bond price = 550.74 + 9052.01 = $9727.75

Therefore, the best choice is (B) $9727.75 as it is the calculated bond price.

What Must Be the Price of a $10,000 Bond with a 6.5