The University of California has two bonds outstanding. Both issues have the same credit rating, a face value of $$1,000$ and a coupon rate of $6\%.$ Coupons are paid twice a year. Bond A matures in $1$ year, while bond B matures in $30$ years.

The market interest rate for similar bonds is $9\%.$

What is the price of bond A$?$

What is the price of bond B$?$

Now assume that yields increase to $12\%.$ What is the price of bond A$?$

What is the price of bond B now?