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There are two bonds in the market, Bond X and Bond Y. Both of them have a face value of $4000, and annual coupon of

There are two bonds in the market, Bond X and Bond Y. Both of them have a face value of $4000, and annual coupon of $400. However, Bond X takes 3 years to maturity and Bond Y take 4 years to maturity.

a) Suppose YTM is 4%, what are the bond prices for them?

b) Suppose YTM is 8%, what are the bond prices? Which bond has a higher interest rate risk?

PLEASE show work for both.

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