What is the yield to maturity of a ten-year,$1000 bond with a 5.2% coupon rate and semi-annual coupons if this bond is currently trading for a price of $884?
A)5.02%
B)6.23%
C)6.82%
D)12.46%
E)5.20%

Question

Quizplus · Accepted Answer

To calculate the yield to maturity (YTM) of the bond, we need to find the discount rate that equates the present value of the expected cash flows from the bond to its current market price.

Step 1: Determine the semi-annual coupon payment
Coupon rate = 5.2%
Face value = $1000
Semi-annual coupon payment = 0.052/2 * 1000 = $26

Step 2: Determine the number of semi-annual coupon periods
Ten-year bond with semi-annual coupons has 20 semi-annual periods.

Step 3: Calculate the present value of each semi-annual coupon payment
PV of each semi-annual coupon payment = (Coupon payment) / (1 + Yield/2)^n
where n is the number of periods until the payment is received (counted in semi-annual periods)

PV of each semi-annual coupon payment = 26 / (1 + YTM/2)^n

Step 4: Calculate the present value of the face value payment at maturity
PV of face value payment = Face value / (1 + Yield/2)^n
where n is the number of periods until maturity (counted in semi-annual periods)

PV of face value payment = 1000 / (1 + YTM/2)^n

Step 5: Find the YTM that satisfies the following equation:
Market price = PV of all semi-annual coupon payments + PV of the face value payment
$884 = PV of each semi-annual coupon payment * 20 + PV of face value payment

Solving the equation using a financial calculator or spreadsheet gives us YTM = 6.82%.

Therefore, the answer is C) 6.82%.

What Is the Yield to Maturity of a Ten-Year,$1000 Bond