Respuesta :
The rule of the loan is
[tex]P=\frac{L(\frac{r}{n})}{\lbrack1-(1+\frac{r}{n})^{-nt}\rbrack}[/tex]P is the monthly payment
L is the loan amount
r is the rate in decimal
n is the number of periods per year
t is the time
Since you afford $1200 per month, then
P = 1200
Since the loan interest is 7%, then
r = 7/100 = 0.07
n = 12
Since the time is 30 years, then
t = 30
Substitute them in the rule above to find L
a)
[tex]\begin{gathered} 1200=\frac{L(\frac{0.07}{12})}{\lbrack1-(1+\frac{0.07}{12})^{-12(30)}\rbrack} \\ 1200\lbrack1-(\frac{1207}{1200})^{-360}\rbrack=L(\frac{0.07}{12}) \\ \frac{1200\lbrack1-(\frac{1207}{1200})^{-360}\rbrack}{\frac{0.07}{12}}=L \\ 180369.0815=L \end{gathered}[/tex]The amount of the loan is $180 369.0815
b)
You can find the total money you will pay the loan company, multiply P by n by t.
[tex]\begin{gathered} \text{Total}=1200\times12\times30 \\ \text{Total}=432000 \end{gathered}[/tex]You will pay a total amount of $432 000
c)
The amount of interest is the difference between the total payment and the amount of the loan
[tex]\begin{gathered} I=T-L \\ I=432000-180369.0815 \\ I=251630.9185 \end{gathered}[/tex]The interest is $251 630.9185
