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) (\( r \)): 13%
- Term (\( n \)): 12 years (or 12 * 12 = 144 months)
- Monthly payment (\( M \)): $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.
