To determine Maricela's monthly payment for the loan of [tex]$18,000 for 5 years at an interest rate of 6.2%, we use the monthly payment formula for an installment loan:
\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]
where:
- \(M\) is the monthly payment.
- \(P\) is the principal loan amount which is $[/tex]18,000.
- [tex]\(r\)[/tex] is the monthly interest rate. The annual interest rate is 6.2%, so the monthly interest rate is [tex]\(\frac{6.2\%}{12} = 0.062 / 12\)[/tex].
- [tex]\(n\)[/tex] is the number of monthly payments. Since the loan is for 5 years, [tex]\(n = 5 \times 12 = 60\)[/tex].
We need to find [tex]\(M\)[/tex].
1. Calculate the monthly interest rate [tex]\(r\)[/tex]:
[tex]\[
r = \frac{0.062}{12} \approx 0.0051667
\][/tex]
2. Calculate the number of monthly payments [tex]\(n\)[/tex]:
[tex]\[
n = 5 \times 12 = 60
\][/tex]
3. Place these values into the monthly payment formula:
[tex]\[
M = \frac{18000 \times 0.0051667 \times (1 + 0.0051667)^{60}}{(1 + 0.0051667)^{60} - 1}
\][/tex]
4. Simplify the expression to get the monthly payment [tex]\(M\)[/tex]:
[tex]\[
M \approx 349.67
\][/tex]
Therefore, Maricela’s monthly payment for the loan is
[tex]\[
\$ 349.67
\][/tex]
