Use PMT $=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$ to determine the regular payment amount, rounded to the nearest dollar. In terms of paying less in interest, which is more economical for a $$150,000$ mortgage: a $30-$year fixed$-$rate at $10\%$ or a $20-$year fixed$-$rate at $9\mathrm{.}5\%?$ How much is saved in interest?

Select the correct choice below and fill in the answer box within your choice.

$($Do not round until the final answer. Then round to the nearest thousand dollars.$)$

A$.$ The $30-$year $10\%$ loan is more economical. The buyer will save approximately $ in interest.

B$.$ The $20-$year $9\mathrm{.}5\%$ loan is more economical. The buyer will save approximately $ in interest.