Question #241494

**a friend of your just invested in an outstanding bond with a 4% annual coupon and a remaining maturity of 5 years. the bond has a per value og $500 and the market interest rate is currently 7%. how much did your friend pay for the bond? is it par, premium or discount bond?**

Expert's answer

Annual coupon=$500*4%

=$20

Hence current price=Annual coupon*present value of annuity factor(7%,5)+$500*present value of discounting factor(7%,5)

Present value of annuity="(\\frac{1-(1+interest\\ rate)^{-time\\ period}}{interest\\ rate})"

="(\\frac{1-(1.04)^{-5}}{0.04})"

=4.451822331

Present value of discounting="\\frac{1}{{(1+rate})^{time\\ period}}"

="\\frac{1}{1.04^{5}}"

=0.8219271068

Present value =$20*4.451822331+$500*0.8219271068

=$89.03644662+$410.9635534

=$500

It sells at it's face value hence a par bond.

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