The buyer of a piece of real estate is often given the option of buying down the loan. This option gives the buyer a choice of loan terms in which various combinations of interest rates and discount points are offered. The choice of how many points and what rate is optimal is often a matter of how long the buyer intends to keep the property.

Darrell Frye is planning to buy an office building at a cost of $$982,000.$ He must pay $10\%$ down and has a choice of financing terms. He can select from a $9\%30-$year loan and pay $4$ discount points, a $9\mathrm{.}25\%30-$year loan and pay $3$ discount points, or a $9\mathrm{.}5\%30-$year loan and pay $2$ discount points. Darrell expects to hold the building for four years and then sell it$.$ Except for the three rate and discount point combinations, all other costs of purchasing and selling are fixed and identical. $($Round your answers to the nearest cent. Use this table, if necessary.$)$

$($a$)$

What is the amount being financed?

$

$($b$)$

If Darrell chooses the $4-$point $9\%$ loan, what will be his total outlay in points and payments after $48$ months?

$

$($c$)$

If Darrell chooses the $3-$point $9\mathrm{.}25\%$ loan, what will be his total outlay in points and payments after $48$ months?

$

$($d$)$

If Darrell chooses the $2-$point $9\mathrm{.}5\%$ loan, what will be his total outlay in points and payments after $48$ months?

$

$($e$)$

Of the three choices for a loan, which results in the lowest total outlay for Darrell after $48$ months?

the $4-$point $9\%$ loan

the $3-$point $9\mathrm{.}25\%$ loan

the $2-$point $9\mathrm{.}5\%$ loan