Question

1. A 30-year bond has a face value of $1,000 and a 9% coupon rate, paid semi-annually. a. You buy the bond today when it has a yield to maturity of 7%. Compute the price of the bond today.

Answer #1

**The price of the bond is computed as shown
below:**

**The coupon payment is computed as follows:**

= 9% / 2 x $ 1,000 (Since the coupon payments are semi annual, hence divided by 2)

**= $ 45**

**The YTM is computed as follows:**

= 7% / 2 (Since the coupon payments are semi annual, hence divided by 2)

**= 3.5% or 0.035**

**N is computed as follows:**

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

**= 60**

**So, the price of the bond will be as
follows:**

**= Coupon payment x [ [ (1 - 1 / (1 + r) ^{n} ] /
r ] + Par value / (1 + r)^{n}**

= $ 45 x [ [ ( 1 - 1 / (1 + 0.035)^{60} ] / 0.035 ] + $
1,000 / 1.035^{60}

= $ 45 x 24.94473412 + $ 126.9343059

**= $ 1,249.45 Approximately**

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

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 6%?
a. $886.9
b. $940.7
c. $1,065.6
d. $1,138.4
e. $1,219.2

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 8%? a. $886.9 b. $940.7 c. $1,065.6 d.
$1,138.4 e. $1,219.2

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

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