Respuesta :
The formula to calculate the monthly mortgage payment is given below as
[tex]M=\frac{P\times r(1+r)^n}{(1+r)^n-1}[/tex]From the question ,
[tex]\begin{gathered} P=80,000 \\ r=\frac{10}{100}=\frac{0.1}{12} \\ n=30\times12=360 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} M=\frac{P\times r(1+r)^n}{(1+r)^n-1} \\ M=\frac{80000\times\frac{0.1}{12}(1+\frac{0.1}{12})^{360}}{(1+\frac{0.1}{12})^{360}-1} \end{gathered}[/tex]By simplifying the expression above, we will have
[tex]\begin{gathered} M=\frac{80000\times\frac{0.1}{12}(1+\frac{0.1}{12})^{360}}{(1+\frac{0.1}{12})^{360}-1} \\ M=\frac{\frac{2000}{3}(\frac{121}{120})^{360}}{(\frac{121}{120})^{360}-1} \\ M=\frac{\frac{2000}{3}\times19.83739937}{19.83739937-1} \\ M=\frac{13224.93292}{18.83739937} \\ M=702.06 \end{gathered}[/tex]Therefore,
The amount to be paid over a year will be
[tex]\begin{gathered} =702.06\times12 \\ =8424.72 \end{gathered}[/tex]Hence,
The amount to be paid over 1 year = $8,424.72
