In the question, we are given that the Sanchez family takes a loan of $200,000 for a fixed annual rate of 4%, 30-year mortgage.
Explanation
We can find the monthly payment using the formula below;
[tex]\text{Fixed monthly payment = }P\times\frac{r}{12}\times\frac{(1+\frac{r}{12})^n}{\lbrack(1+\frac{r}{12})^n-1)}[/tex]Where the principal (p) = $200,000, the annual rate = 4% and number of payment installments = 30 x 12 =360
[tex]\begin{gathered} \text{FMP = 200000 x }\frac{\text{4}}{12}\text{ x }\frac{\text{(1+}\frac{0.04}{12})^{360}}{\lbrack\text{(1+}\frac{0.04}{12})^{360}-1\rbrack} \\ \text{FMP = 200000 x }\frac{\text{4}}{12}\text{ x }\frac{\text{(301/300})^{360}}{\lbrack\text{(301/300})^{360}-1\rbrack} \\ \text{FMP = 200000 x }\frac{4}{12}\text{ x }\frac{\text{(301/300})^{360}}{\lbrack\text{(301/300})^{360}-1\rbrack} \\ \text{FMP}=954.83 \end{gathered}[/tex]Answer: The monthly payment is $954.83
