refers to the bonds of the Apollo Corporation, all of which have a call feature. The call feature allows Apollo to pay off bonds anytime after the first $15$ years, but requires that bondholders be compensated with an extra year's interest at the coupon rate if such a payoff is exercised.

$17.$ Apollo's Alpha bond was issued $10$ years ago for $30$ years with a face value of $$1,000.$ Interest rates were very high at the time, and the bond's coupon rate is $20\%.$ The interest rate is now $10\%.$

a$.$ At what price should an Alpha bond sell?

b$.$ At what price would it sell without the call feature?