To calculate Maricela's monthly payment for the loan, we use the following monthly payment formula:
[tex]\[M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}\][/tex]
where:
- [tex]\(M\)[/tex] is the monthly payment,
- [tex]\(P\)[/tex] is the principal loan amount,
- [tex]\(r\)[/tex] is the monthly interest rate,
- [tex]\(n\)[/tex] is the number of total monthly payments.
Given values:
- Principal amount [tex]\(P = \$18,000\)[/tex],
- Annual interest rate [tex]\(6.2\%\)[/tex],
- Loan term [tex]\(5\)[/tex] years.
First, convert the annual interest rate to a monthly interest rate by dividing by 12:
[tex]\[r = \frac{6.2\%}{12} = \frac{0.062}{12} = 0.0051667\][/tex]
Next, calculate the number of monthly payments over the term of the loan:
[tex]\[n = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ months}\][/tex]
Now, substitute these values into the monthly payment formula:
[tex]\[M = \frac{18000 \cdot 0.0051667 \cdot (1 + 0.0051667)^{60}}{(1 + 0.0051667)^{60} - 1}\][/tex]
Upon solving the above equation, we find:
[tex]\[M \approx 349.67\][/tex]
Thus, Maricela's monthly payment for the loan is [tex]\( \boxed{349.67} \)[/tex].
