Two $20-$year maturity mortgage$-$backed bonds are issued. The first bond has a par value of $$10,000$ and promises to pay a $10\mathrm{.}5$ percent annual coupon, while the second is a zero coupon bond that promises to pay $$10,000($par$)$ after $20$ years, with interest accruing at $10\mathrm{.}0$ percent. At issue, bond market investors require a $12\mathrm{.}0$ percent interest rate on both bonds.

Required:

a$.$ What is the initial price on each bond?

b$.$ Now assume that both bonds promise interest at $10\mathrm{.}5$ percent, compounded semiannually. What will be the initial price for each bond?

c$.$ If market interest rates fall to $9\mathrm{.}5$ percent at the end of the fifth year, what will be the value of each bond, assuming annual payments as in $($a$)($state both as a percentage of par value and actual dollar value$)?$