Question

Yolanda took out a 30-year mortgage for $80,000 at 10% How much wills he pay over one year?

Answer 1

The formula to calculate the monthly mortgage payment is given below as

`M=(P* r(1+r)^n)/((1+r)^n-1)`

From the question ,

`\begin{gathered} P=80,000 \\ r=(10)/(100)=(0.1)/(12) \\ n=30*12=360 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} M=(P* r(1+r)^n)/((1+r)^n-1) \\ M=(80000*(0.1)/(12)(1+(0.1)/(12))^(360))/((1+(0.1)/(12))^(360)-1) \end{gathered}`

By simplifying the expression above, we will have

`\begin{gathered} M=(80000*(0.1)/(12)(1+(0.1)/(12))^(360))/((1+(0.1)/(12))^(360)-1) \\ M=((2000)/(3)((121)/(120))^(360))/(((121)/(120))^(360)-1) \\ M=((2000)/(3)*19.83739937)/(19.83739937-1) \\ M=(13224.93292)/(18.83739937) \\ M=702.06 \end{gathered}`

Therefore,

The amount to be paid over a year will be

`\begin{gathered} =702.06*12 \\ =8424.72 \end{gathered}`

Hence,

The amount to be paid over 1 year = $8,424.72