On January $1,2020,$ the Q$-$Ball Company issued $$200,000$ bonds with an $8\%$ stated interest rate. Each $$1,000$ bonds pay interest on June $30$ and December $31.$ The bonds mature on December $31,2029.$

Required:

a$.$ Assume the bonds were sold for $$175,075\mathrm{.}58$ to yield $10\%.$ Prepare a bond amortization schedule for the first year of the bond life using the effective interest method.

b$.$ Prepare the journal entry for paying the interest on December $31,2020.$

c$.$ Why did these bonds originally sell at a discount?