Question

A bond with 10 years to maturity has a face value of $1,000. The bond pays an 8 percent semiannual coupon, and the bond has a 5.9 percent nominal yield to maturity. What is the price of the bond today?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 8% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 40

The YTM will be as follows:

= 5.9% / 2 (Since the payments are semi annually, hence divided by 2)

= 2.95% or 0.0295

N will be as follows:

= 10 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 20

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

= $ 40 x [ [ (1 - 1 / (1 + 0.0295)²⁰ ] / 0.0295 ] + $ 1,000 / 1.0295²⁰

= $ 40 x 14.94648325 + $ 559.0787441

= $ 1,156.94 Approximately

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