You purchase a home with a $5\%/$year fixed$-$rate, $30-$year mortgage. Interest is compounded monthly. The amount borrowed is $$300,000.$ Every three months, you make an additional quarter payment which is used to pay off principal $($e$.$g$.,$ at EOM $1$ payment $=$ A$,$ at EOM $2$ payment $=$ A$,$ at EOM $3$ payment $=1\mathrm{.}25$A$).$ How long will it take to pay off the mortgage? Include a cash flow diagram in your written work. Hints: The present worth of the sequence of payments must equal the amount borrowed. You can divide the payments into three parts: a uniform series paid monthly, a uniform series paid quarterly, and a single final payment that may be smaller than the typical payment.The answer is an integer. You must enter the exact answer.

B$)$ what is the total amount of interest paid over the life of the loan?