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?

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.