Answer:
Interest portion of first payment = $1,050
(83.28% of the first payment goes towards interest).
Step-by-step explanation:
To determine how much of the first payment goes toward interest, we can use the formula for calculating the interest portion of a loan payment:
[tex]\boxed{\textsf{Interest for the month} = \textsf{Outstanding loan balance} \times \textsf{Monthly interest rate}}[/tex]
The outstanding loan balance is the amount of the loan that still needs to be paid off, and the monthly interest rate is the annual interest rate divided by 12 (since the loan is paid monthly).
As we wish to calculate how much of the first payment goes towards interest, the outstanding balance at this point is the original balance of $84,000. Given that the interest rate is 15%, then:
[tex]\textsf{Interest for the 1st month} = \$84000 \times \dfrac{15\%}{12\; \textsf{months}} \\\\\\ \textsf{Interest for the 1st month} = \$84000 \times \dfrac{0.15}{12} \\\\\\ \textsf{Interest for the 1st month}=\$84000 \times 0.0125 \\\\\\ \textsf{Interest for the 1st month}=\$1050[/tex]
So, $1,050 of the first payment of the loan goes towards interest.
Additional Notes
In terms of a percentage, $1,050 is approximately 83.28% of the monthly loan payment of $1,260.74, so 83.28% of the first payment goes towards interest.