Question

a bond has a face value of $1000 and 14 years until maturity. the bond has a 3% APR coupon with semi- annual coupon payments. currently, investors seek a 6% APR yield to maturity to hold the bond. what is the current trading price of the bond?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 3% / 2 x $ 1,000 (As the payments are semi annually, hence divided by 2)

= $ 15

The YTM will be as follows:

= 6% / 2 (As the payments are semi annually, hence divided by 2)

= 3% or 0.03

N will be as follows:

= 14 x 2 (As the payments are semi annually, hence multiplied by 2)

= 28

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

= $ 15 x [ [ (1 - 1 / (1 + 0.03)²⁸ ] / 0.03 ] + $ 1,000 / 1.03²⁸

= $ 15 x 18.76410823 + $ 437.0767532

= $ 718.54

Do ask in case of any doubts.