$5.$ A corporation issues $$7,500,000$ of $8\%$ bonds to yield interest at the rate of $7\%.($a$)$ Was the amount of cash received from the sale of the bonds greater or less than $$7,500,000?($b$)$ Identify the following terms related to the bond issue: $(1)$ face amount, $(2)$ market or effective rate of interest, $(3)$ contract rate of interest, and $(4)$ maturity amount.