From the statement of the problem, we know the following data of the mortgage:
• t = time = 30 years,
,• P = principal = $100,000,
,• r = interest rate in decimal = 7/100 = 0.07.
The monthly payments are given by the following formula:
[tex]m=\frac{P\cdot\frac{r}{12}}{1-(1+\frac{r}{12})^{-t\cdot12}}\text{.}[/tex]Replacing the data of the problem, we find that the monthly payments will be:
[tex]m=\frac{100,000\cdot\frac{0.07}{12}}{1-(1+\frac{0.07}{12})^{-30\cdot12}}\cong665.302.[/tex]dollars.
The money that Aaron will pay in a year is 12 times the value of the monthly payment:
total of a year = 12 * $665.302 ≅ $7983.63.
Answer
Aaron will pay $7983.63 in a year.
