Question

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

Answer 1

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