Bond Pricing and Yield to Maturity

A U$.$S$.$ Treasury bond $($T$-$bond$)$ that matures in $3$ years has a face value of $$1000,$ a $6\%$ coupon rate $($which is coupon payment

as a percentage of the face value$)$ expressed as an SAIR $($Stated annual interest rate$)$ and semi$-$annual coupon

payments. The effective semi$-$annual market interest rate is $5\%.$

a$)$ What price should the bond sell for?

b$)$ Investors learn that the central bank will reduce interest rates so that the effective semi$-$annual market interest rate falls to

$1\%.$ What should be the new price of the bond?

c$)$ At what interest rate would the bond 'sell at par' $($that is the bond price equals the face value$)?$

d$)$ Now assume that bond investors believe that market interest rates will be $1\%$ for the next $1,5$ years and $5\%$ thereafter.

What should the US government bond sell for under these assumptions?

e$)$ Given the bond price you determined in part $($d$)$ what would be the implied yield to maturity of the bond?