Respuesta :
Answer:
a. The monthly payment is approximately $2,751.62
b. The total of all monthly payment for the 30 years is approximately $990,582.175
c. The finance charge is approximately $615,582.175
d. The interest is greater than the original cost of the home
Step-by-step explanation:
a. The given parameters for the mortgage are;
The principal amount of the home Fernandez family is buying, P = $375,000
The number of years mortgage they take buy the home = 30 years
The percentage rate of the mortgage, r = 8%
The monthly payment, 'A', for the mortgage is given as follows;
[tex]A = \dfrac{ P \times \left (\dfrac{r}{12} \right ) \times\left (1 + \dfrac{r}{12} \right )^n}{\left (1 + \dfrac{r}{12} \right )^n - 1 }[/tex]
Where;
n = The number of monthly payments = 30 years × 12 months/year = 360 months
Therefore, by substituting the known values, we have;
[tex]A = \dfrac{ 375,000 \times \left (\dfrac{0.08}{12} \right ) \times\left (1 + \dfrac{0.08}{12} \right )^{360}}{\left (1 + \dfrac{0.08}{12} \right )^{360} - 1 } = 2,751.61715172[/tex]
The monthly payment, A = $2,751.61715172 ≈ $2,751.62
b. The total of all monthly payment for the 30 years = 360 × $2,751.61715172 ≈ $990,582.175
c. The finance charge = The total amount repaid - The amount that was financed = The interest payed on the amount financed
∴ The finance charge = $990,582.175 - $375,000 ≈ $615,582.175
d. The interest (approximately $615,582.175) is greater than the original cost of the home ($375,000)
