$(5$ points$)$ You took an interest$-$only $$30,000$ S$-$year loan at the interest rate $($APR$)$ of $8\%$ per year. One year later, the interest rate dropped from $8\%$ to $7\%.$ The refinancing cost is $$800.$

a$.(1\mathrm{.}5$ points$)$ Complete an amortization table of the original loan.

b$.(0\mathrm{.}5$ point$)$ What is the contractual value of the loan in Year $1?$

c$.(1$ point$)$ What is the market value of the loan in Year $1?$

$(0\mathrm{.}5$ point$)$ What is the amount of gain$/$loss from refinancing in Year $1?$

$$ Should you refinance the loan? Explain why.

$(1\mathrm{.}5$ points$)$ Complete an amortization table of the new loan $-$ still an interest$-$only loan but at $7\%.$