Question

Greenwich store has a bond that matures in 10 years and has a coupon rate of 8 percent. The interest is paid semiannually and the face value is 1000. What is the market price of the bond if the yield to maturity is 7 percent?

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 being made semi annually, hence divided by 2)

= $ 40

The YTM is computed as follows:

= 7% / 2 (Since the payments are being made semi annually, hence divided by 2)

= 3.5% or 0.035

N is computed as follows:

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

= 20

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

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

= $ 40 x [ [ (1 - 1 / (1 + 0.035)²⁰ ] / 0.035 ] + $ 1,000 / 1.035²⁰

= $ 40 x 14.2124033 + $ 502.5658844

= $ 1,071.06 Approximately

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