Final answer:
After missing two quarterly payments of $450 on a $10,000 loan with a 9% yearly interest, and with the third payment due, the borrower would owe approximately $10,905.06 without considering any late penalties. This amount includes interest compounded quarterly over the nine months. Specific penalties for missing payments would depend on the loan agreement and are not factored into this calculation.
Step-by-step explanation:
To calculate the current amount owed on the loan, including missed payments and interest, we must first determine how much interest has accumulated on the unpaid balance.
Since the payments are quarterly, the annual interest rate of 9% should be divided by four to get the quarterly rate, which is 2.25%.
The interest for one quarter on $10,000 is 10,000 × 0.0225 = $225.
After missing two payments over nine months, two quarters have passed. The unpaid balance after the first quarter, including interest, is $10,225 (initial loan plus interest).
This new balance further accrues interest for another quarter, resulting in $10,225 × 1.0225 = $10,455.06 rounded to the nearest cent. So, after the second quarter, the total balance, including interest on the new amount, is approximately $10,455.06.
The third payment of $450 is now due, bringing the total to pay at this point to $10,455.06 + $450 = $10,905.06.
However, penalties on the missed payments have not been specified in the question, so assuming there are late fees (which can vary widely), these would add to the total owed.
The penalties would depend on the specific terms of the loan agreement. If we ignore any potential penalties, the amount owed is $10,905.06.