Use the information below to answer question $12$ and $13$

The Williams purchased a home for $$240,000.$ They made a $15\%$ down payment and borrowed the rest at $5\%$ interest compounded monthly on a $20$ year loan. Their monthly payments are $$1,346\mathrm{.}31$

$12.$ How much did the Williams borrow for buying their home?

A$)$ $$204,000$

B$)$ $$238,653\mathrm{.}69$

C$)$ $$36,000$

D$)$ $$192,000$

E$)$ $$240,000$

$13.$ After making their first payment, how much will the Williams still owe on the house? $[$Hint: Make the first line of an amortization table to help answer this question$]$

A$)$ $$239,653\mathrm{.}69$

B$)$ $$203,503\mathrm{.}69$

C$)$ $$202,653\mathrm{.}69$

$($D$)$ $$238,653\mathrm{.}69$

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