In this problem we are going to calculate bond prices and returns

Suppose that the yield on a $3$ year note is $2\mathrm{.}5\%.$

a$)(10$ points$)$ Calculate the price of the $3$ year note $($face value $=$$$1000)$ with three annual coupon payments $($after year $1,$ after year $2,$ after

year $3)$ of $$30,$ i$.$e$.,$ the coupon rate is $3\mathrm{.}0\%.$

b$)(5$ points$)$ Is this note selling at a discount or premium? Explain.

Suppose that after one year and after you receive one coupon payment, you decide to sell your note. Your note is now a two year note with

one coupon payment after $1$ year and another after year $2.$ Consider the following two scenarios:

Scenario #$1-$ interest rates on what is now a two year note $($i$.$e$.,$ your note$)$ have fallen to $1\mathrm{.}00\%$

Scenario #$2-$ interest rates on what is now a two year note $($i$.$e$.,$ your note$)$ have risen to $4\%$

c$)(10$ points$)$ Calculate the price that you can sell your note for under scenario #$1$ and the associated rate of return when you sell your note

given Scenario #$1$

d$)(10$ points$)$ Calculate the price that you can sell your note for under scenario #$2$ and the associated rate of return when you sell your not

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