You are considering a 10-year, $1,000 par value bond. Its coupon rate is 8%, and interest is paid semiannually. If you require an “effective” annual interest rate (not a nominal rate) of 7.1225%, how much should you be willing to pay for the bond?

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TomShelby TomShelby · Answer 1 · 2019-07-21T01:21:10+02:00

Answer:

$1,061.28

Explanation:

We need to calculate the present value of the bond using the minimum effective rate of 7.1225%

First we calcualte the present value of an annuity of $80 for 10 years

[tex]C * \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

[tex]80 * \frac{1-(1+7.1225%)^{-10} }{7.1225%} = PV\\[/tex]

PV = $558.72

Then we calculate the $1,000 in 10 years present value

[tex]\frac{Principal}{(1 + rate)^{time}}= PV[/tex]

[tex]\frac{1,000}{(1 + 7.1225%)^{10} } = PV[/tex]

PV = $502.57

Then we add both values

$502.57 + $558.72 = $1,061.28

This will be the present value AKA market price which yields the minimun rate of 7.1225%