Use $\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$ to determine the regular payment amount, rounded to the nearest dollar. Consider the following pair of mortgage loan options for a $$145,000$ mortgage. Which mortgage loan has the larger total cost $($closing costs $+$ the amount paid for points $+$ total cost of interest$)?$ By how much?

Mortgage A: $15-$year fixed at $6\mathrm{.}25\%$ with closing costs of $$2200$ and $1$ point.

Mortgage B: $15-$year fixed at $4\mathrm{.}5\%$ with closing costs of $$2200$ and $5$ points.

Choose the correct answer below, and fill in the answer box to complete your choice.

$($Do not round until the final answer. Then round to the nearest dollar as needed.$)$

A$.$ Mortgage A has a larger total cost than mortgage B by $

B$.$ Mortgage B has a larger total cost than mortgage A by $