Call $$Bond A$$ a US Treasury $30-$year bond that was issued with a $10\%$ coupon on Dec $31,1980.$ On Dec $31,2000$ this

is now a $10-$year maturity bond. Suppose prevailing interest rates are $4\%.$

a$.$ What is the fair market price for Bond A$?$

b$.$ The US Treasury issued $$Bond B$,$ a new $10-$year bond on December $31,2000$ with a $4\%$ coupon. What is the

fair market price of this bond?

c$.$ As an investor, which bond would you prefer to purchase?

d$.$ Sketch out the price curve for both Bond A and Bond B$.$ That is$,$ show a chart with Price on the y$-$axis and

YTM on the x$-$axis $($similar to Slide $17$ in $$Fixed Income Part $1$ lecture slides$).$ Vary your YTM from $1\%$ to $12\%,$

and plot the resulting prices for each bond.

e$.$ Calculate the duration for both bond A and bond B

f$.$ Discuss any differences between Bond A and Bond B on the chart you produced and why you think they

might arise.