Question

# Question 18 What is the price of a 30-year, 7% coupon rate, \$1,000 face value bond...

Question 18

What is the price of a 30-year, 7% coupon rate, \$1,000 face value bond that pays interest semi-annually, if the yield to maturity on similar bonds is 7.5%?

 a. \$886.9 b. \$940.7 c. \$1,065.6 d. \$1,138.4 e. \$1,219.2

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 7% / 2 x \$ 1,000 (Since the payments are semi annually, hence divided by 2)

= \$ 35

The YTM will be as follows:

= 7.5% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.75% or 0.0375

N will be as follows:

= 30 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 60

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)n ] / r ] + Par value / (1 + r)n

= \$ 35 x [ [ (1 - 1 / (1 + 0.0375)60 ] / 0.0375 ] + \$ 1,000 / 1.037560

= \$ 35 x 23.73791594 + \$ 109.8281522

= \$ 940.7 Approximately

So, the correct answer is option b.

Feel free to ask in case of any query relating to this question

#### Earn Coins

Coins can be redeemed for fabulous gifts.