Calculate the price of a zero coupon with 10 years maturity, par value 100$ assuming that the 10-year zero coupon rate is 5%, the default and recover probabilities are 50%, and recovery rate of 50%. Is the price lower or higher of the same bond in the previous point? Why?

Consider the same bond but with default probability of 0%, recover probability of 100% and recovery rate of 50%. Is the price the same? Why?