Use the following information to answer the question$($s$)$ below.

Dagny Taggart has just purchased a home and taken out a $$400,000$ mortgage. The mortgage has a $30-$year term with monthly payments and has an APR of $5\mathrm{.}4\%.$

The total amount of principal that Dagny will pay during the first three months of her mortgage is closest to:

Show all work, show how to do this on excel and by hand.