Simon Pause Corporation bonds have a zero$-$coupon rate, mature in ten years, and have a current yield to maturity of $5\%$ annual rate, compounded semiannually.

a$.$ What is the price per $$100$ of face value of Simon Pause Corporation bonds?

b$.$ Suppose in three years the market price of the bond is $66\mathrm{.}11178$ per $$100$ of face value. What will the yield to maturity be at that time?

c$.$ Suppose you purchased the Simon Pause bond today and sold the bonds in three years for $66\mathrm{.}11178$ per $$100$ of face value. What is your holding period yield for this investment?

Hint: The holding period yield is defined as the interest rate that sets the price of a bond equal to the present value of the realized cash flows the investor received from holding the bond. $($The holding period yield will equal the yield to maturity for an investor who buys a bond and holds the bond until maturity$).$