The Pennington Company issued a new series of bonds on January $1,1989.$ The bonds were sold at par $($$$1000),$ had a $12\%$ coupon, and matured in $30$ years on December $31,2018.$ Coupon payments are made semiannually $($on June $30$ and December $31)$ a$.$ What was the Yield to maturity $($YTM$)$ on the date the bonds were issued? b$.$ What was the price of the bonds on January $1,1994(5$ years later$),$ assuming that interest rates had fallen to $10\%?$