Question

Fred takes out a mortgage for $60,000 at 7% for 20 years. What are his monttpayment, the total amount paid, and the cost of the mortgage?

Answer 1

We will have the following:

First, we determine the monthly rate:

`r_m=(0.07)/(12)=(7)/(1200)`

Now, we determine the monthly payment:

`\begin{gathered} A=P((1+r_m)^n)/((1+r_m)^n-1) \\ \\ \Rightarrow A=60000\frac{(1+(7/1200))^{^(240)}}{(1+(7/1200))^(240)-1}\Rightarrow A\approx465.18 \end{gathered}`

So, the monthly payment will be approximately $465.18.

The total amount paid will be:

`\begin{gathered} X=A\ast n\ast t \\ \\ \Rightarrow X=(465.18)(12)(20)\Rightarrow X\approx111643.2 \end{gathered}`

So, the total payment will be approximately $111 643.2.

The cost of the mortgage is:

`c=111643.2-60000\Rightarrow c\approx51643.2`

So, the cost of the mortgage is approximately $51 643.2.