IOU Corporation wants to issue two bonds: a zero$-$coupon bond and a coupon bond. The zero$-$coupon bond has a maturity of $10$ years and is discounted annually while the coupon paying bond has a maturity of $20$ years and pays coupons on a monthly basis. The annual yield$-$to$-$maturity $($YTM$)$ on $10$ year U$.$S$.$ government bonds is $3\%$ while the annual YTM on $20$ year coupon paying U$.$S$.$ government bonds is $4\%($The government bond also pays coupons on a monthly basis$).$ In addition, the credit spread on $10$ year zero$-$coupon bonds is $3\%,$ while the credit spread on $20$ year coupon paying bonds is $4\%.$ Both bonds have a face value of $$100.$ In addition, the coupon paying bond has a coupon rate of $5\%.$ Based on this information, answer the following questions.

Which of the following would be the price of the $10$ year zero$-$coupon bond issued by IOU Corporation?

A$.$ $$74\mathrm{.}62$

B$.$ $$55\mathrm{.}86$

C$.$ $$61\mathrm{.}35$

D$.$ $$67\mathrm{.}57$

Which of the following expressions would correctly calculate the current price $(P_0)$ of the coupon paying bond issued by IOU Corporation?

A$.P_0=\frac{5}{0\mathrm{.}006}(1-\frac{1}{(1+0\mathrm{.}006{)}^{240}})+\frac{100}{(1+0\mathrm{.}006{)}^{240}}$

B$.P_0=\frac{0\mathrm{.}41}{0\mathrm{.}006}(1-\frac{1}{(1+0\mathrm{.}006{)}^{240}})+\frac{100}{(1+0\mathrm{.}006{)}^{240}}$

c$.P_0=\frac{0\mathrm{.}41}{0\mathrm{.}08}(1-\frac{1}{(1+0\mathrm{.}08{)}^{240}})+\frac{100}{(1+0\mathrm{.}08{)}^{240}}$

D$.P_0=\frac{5}{0\mathrm{.}08}(1-\frac{1}{(1+0\mathrm{.}08{)}^{240}})+\frac{100}{(1+0\mathrm{.}08{)}^{240}}$