Answered

Suppose you borrow $45,000 at 13% APR for a 12-year term to be paid

monthly. Your monthly payment is $500.00.

How much of your first payment goes toward interest?

How much of this payment goes toward the principal?

Make sure you answer both questions and show your work to earn full

credit.

Interest allocation formula if needed:

Verified Answer :

To find out how much of the first payment goes toward interest and how much goes toward the principal, we can use the following formula:

\[ \text{Interest for the month} = \text{Outstanding Principal} \times \text{Monthly Interest Rate} \]

\[ \text{Principal Payment for the month} = \text{Total Monthly Payment} - \text{Interest for the month} \]

Given:

- Principal amount borrowed (\( P \)): $45,000

- Annual Percentage Rate (APR) (@@MATH_TOKEN_12@@): 13%

- Term (@@MATH_TOKEN_13@@): 12 years (or 12 * 12 = 144 months)

- Monthly payment (@@MATH_TOKEN_14@@): $500.00

First, we need to calculate the monthly interest rate (\( r_{\text{monthly}} \)):

\[ r_{\text{monthly}} = \frac{r}{12} \]

\[ r_{\text{monthly}} = \frac{13}{12 \times 100} \]

\[ r_{\text{monthly}} = \frac{0.13}{12} = 0.0108333 \]

Now, we can calculate the interest for the first month:

\[ \text{Interest for the first month} = P \times r_{\text{monthly}} \]

\[ \text{Interest for the first month} = 45,000 \times 0.0108333 \]

\[ \text{Interest for the first month} ≈ 487.50 \]

Now, we can calculate the principal payment for the first month:

\[ \text{Principal Payment for the first month} = M - \text{Interest for the first month} \]

\[ \text{Principal Payment for the first month} = 500 - 487.50 \]

\[ \text{Principal Payment for the first month} = 12.50 \]

So, in the first payment:

- Approximately $487.50 goes toward interest.

- Approximately $12.50 goes toward the principal.

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