what is the balance on an amortized loan of $780,000 after the first payment if the interest rate is 5% with a monthly P&I payment of $3,780?

$779,500

Explanation:

The  Principal and Interest payment (P&L) as the name implies, include both the interest and the principal.

The interest is calculated based on the loan balance(loan still owed) and the rest will go towards settling the loan.

Interest = 5%/ 12 months * 780,000

= $3,250

Principal = 3,750 - 3,250

= $500

Balance on loan:

= 780,000 - 500

= $779,500