On January $1$ of year $1,$ Arthur and Aretha Franklin purchased a home for $$1\mathrm{.}74$ million by paying $$240,000$ down and borrowing the remaining $$1\mathrm{.}50$ million with a $4\mathrm{.}6$ percent loan secured by the home. The Franklins paid interest only on the loan for year $1,$ year $2,$ and year $3($unless stated otherwise$).$

Note: Enter your answers in dollars and not in millions of dollars. Do not round intermediate calculations. Leave no answer blank. Enter zero if applicable.

a$.$ What is the amount of interest expense the Franklins may deduct in year $3$ assuming year $1$ is $2017?$

b$.$ What is the amount of interest expense the Franklins may deduct in year $2$ assuming year $2$ is $2022?$

c$.$ Assume that year $1$ is $2023$ and that in year $2,$ the Franklins pay off the entire loan, but at the beginning of year $3,$ they borrow $$320,000$ secured by the home at a $5$ percent rate. They make interest$-$only payments on the loan during the year, and they use the loan proceeds for purposes unrelated to the home. What amount of interest expense may the Franklins deduct in year $3$ on this loan?