John needs $$1,000,000$ to retire in five years. There is an annual zero$-$coupon bond with a par$-$value $$1,000$ that matures in $8$ years,

and has a YTM of $12\mathrm{.}75\%.$

If John buys the bond and the YTM stays at $12\mathrm{.}75\%$ then what is the price of the bond in $5$ years?

How many bonds does John need to buy so he can retire in $5$ years with his $$1,000,000$ goal?

If John buys the bond and the YTM stays at $12\mathrm{.}75\%$ when he sells the bond in $5$ years, how much money will John have for retirement?

If John buys the bond and the YTM moves to $10\mathrm{.}75\%$ at what price will he sell the bond for in $5$ years?

If John buys the bond and the YTM moves to $10\mathrm{.}75\%$ when he sells the bond in $5$ years, how much money will John have for

retirement?

If John buys the bond and the YTM moves to $14\mathrm{.}75\%$ at what price will he sell the bond for in $5$ years?

If John buys the bond and the YTM moves to $14\mathrm{.}75\%$ when he sells the bond in $5$ years, how much money will John have for

retirement?

What is the current price of the $8$ year zero$-$coupon bonds if the $12\mathrm{.}75\%?$

How much does John need to invest today if the bonds YTM is $12\mathrm{.}75\%$ and he wants to reach his five year goal of $$1,000,000?$