Biochemical Corporation requires $$570,000$ in financing over the next three years. The firm can borrow the funds for three years at $12\mathrm{.}80$ percent interest per year. The CEO decides to do a forecast and predicts that if she utilizes short$-$term financing instead, she will pay $9\mathrm{.}50$ percent interest in the first year, $14\mathrm{.}25$ percent interest in the second year, and $10\mathrm{.}75$ percent interest in the third year. Assume interest is paid in full at the end of each year.

a$.$ Determine the total interest cost under each plan.

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$\backslash$table$[[,$Interest Cost$],[$Long$-$term fixed$-$rate,$],[$Short$-$term variable$-$rate,$]]$

b$.$ Which plan is less costly$?$

Long$-$term fixed$-$rate plan

Short$-$term variable$-$rate plan