Answered

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Suppose you borrow [tex]$84,000 at 15% APR for a 12-
year term to be paid monthly. Your monthly pay-
ment is $[/tex]1,260.74. How much of the first payment
goes toward interest?

Sagot :

GinnyAnswer
Sure, let's break down the problem step by step:

1. Loan Details Given:
- Loan amount: [tex]$84,000 - Annual interest rate: 15% - Monthly payment: $[/tex]1,260.74

2. Calculate the Monthly Interest Rate:
- The annual interest rate of 15% needs to be converted to a monthly interest rate.
- Monthly interest rate = Annual interest rate / 12
- Monthly interest rate = 0.15 / 12 = 0.0125

3. Determine the Interest Portion of the First Payment:
- The interest portion for the first month is calculated by multiplying the loan amount by the monthly interest rate.
- Interest for the first payment = Loan amount Monthly interest rate
- Interest for the first payment = [tex]$84,000 0.0125 = $[/tex]1,050.00

Thus, [tex]$1,050.00 of the first payment of $[/tex]1,260.74 goes towards interest. The remainder of the payment reduces the principal amount.
semsee45

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.

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