Question

Say that you (or your parents) are purchasing a house for $235,000 and have an excellent credit score. If you pay $1,678.93 at the end of the first month, how much is applied to the principal balance?

Answer 1

It seems the real problem here is
1) determining the amount of time
2) determining the interest rate
Using a loan payment calculator, http://www.1728.org/mortmnts.htm
we determine that $235,000.00 financed for 30 years at a 7.7215% interest rate yields a monthly payment of $1,678.94

When financing a mortgage, (for example 30 years) in the early years of the mortgage, the vast majority of the payment goes to interest.
So, for your first payment, of $1,678.94, the amount going to interest is $1,512.13 and the amount going to principal is  $166.81.

Basically, after spending  $1,678.94 on your first mortgage payment, you actually own (the equity) $166.81.