A firm issued a new series of bonds on January $1,1992.$ The bonds were sold at par $($$$1,000),$ have a $12$ percent coupon, and mature in thirty years. Coupon payments are made semi$-$annually $($on June $30$ and December $31).$

$($a$)$ What was the yield to maturity of the bond on $\frac{1}{1}\frac{?}{92}?$

$($b$)$ Calculate the price of the bond on $\frac{1}{1}\frac{?}{97},$ five years later, assuming that the level of interest rate has fallen to $10\%.$

$($c$)$ If$,$ on July $1,2012,$ an investor expects the bonds to sell for $$896\mathrm{.}64.$ What is the expected yield to maturity on the bonds at that date?