$[$Ch $6]$ Use the following information to answer the questions $12$ through $15$ below.

In October $1981$ Jolene purchased a home at a price of $$300,000.$ She made a $25\%$ cash down payment and financed the balance with a $30-$year fixed$-$rate mortgage with monthly payments at an APR of $18\mathrm{.}63\%$ compounded monthly $($that was the average mortgage rate in Oct. $1981!).$

$12.$ What was her monthly payment?

$($to nearest $$0\mathrm{.}01)$

$13.$ How much of the $1$st monthly payment went towards principal?

$($to nearest $$0\mathrm{.}01)$

$14.$ Suppose it is $15$ years later and Jolene has now made $50\%$ of the payments $($i$.$e$.,$ she just made her $180$ th payment$).$ What percent of the original $$225,000$ principal remains to be paid? ${?}^1$

$($to nearest $0\mathrm{.}001\%)$

$15.$ How much does the principal get reduced during the $27$ th year of the mortgage $($payments #$313$ through #$324)?$

$($to nearest $$0\mathrm{.}01)$