Mr$.$ Smith bought $325$ acres of land at $$3,968$ per acre. He paid $20$ percent down and obtained a loan for the remainder of the cost at $8\mathrm{.}2$ percent over $20$ years. He was to pay off the principal in equal annual payments. The annual interest was to be paid semiannually. He planted $150$ acres in corn that cost him $$3\mathrm{.}00$ per bushel to produce. He had a good year with a yield of $160$ bushels per acre. He was able to sell his corn for $$5\mathrm{.}72$ per bushel. He planted $140$ acres in soybeans.

a$.$ What was the amount of the first$-$year payment?

b$.$ What was the profit from the corn?

c$.$ How much more is needed to make the annual payment after the pro Go fit from the corn is paid on the loan?

d$.$ Is it possible to make enough on the soybeans to pay the balance on the loan? Explain.