Answer
See below
Work Step by Step
(a)
The amount of down payment is computed by multiplying the price of the house to the percent asked for the down payment. Calculate the down payment as mentioned below-
\[\begin{align}
& \text{Down payment}=\text{Price of the house}\times \text{Percent of down payment} \\
& =\$240,000\times20percent\\&=\$240,000\times0.20\\&=\$48,000\end{align}\]
(b)
The amount of mortgage is computed by subtracting the amount of down payment from the price of the house. Compute the mortgage amount as mentioned below-
\[\begin{align}
& \text{Mortgage amount}=\text{Price of the house}-\text{Down payment} \\
& =\$240,000-\$48,000\\&=\$192,000\end{align}\]
(c)
The cost of two points at closing is computed by multiplying the amount of mortgage from to the percent of points at closing. Compute the mortgage amount as mentioned below-
\[\begin{align}
& \text{Cost of two points at closing}=\text{Amount of mortgage}\times \text{percent of points at closing} \\
& =\$192,000\times0.02\\&=\$3,840\end{align}\]
(d)
Calculation of the monthly payments can be done by using formula:
\[PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]}\]
Where P denotes the Principal amount, R denotes the rate of interest, t denotes the number of years and n denotes the number of times compounding is done in a year.
Compute the value of deposit by substituting the values in the formula as mentioned below:
\[\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\
& =\frac{\$192,000\left(\frac{0.07}{12}\right)}{\left[1-{{\left(1+\frac{0.07}{12}\right)}^{-12\times30}}\right]}\end{align}\]
Solve and simplify the equation as follows:
\[\begin{align}
& PMT=\frac{\$192,000\times\left(0.00583\right)}{\left[1-{{\left(1+0.035\right)}^{-360}}\right]}\\&=\frac{\$1,119.36}{0.876647}\\&=\$1,277\end{align}\]
(e)
Computation of the interest amount can be done by deducting the amount of the loan from the total of monthly payments. Compute the amount of interest using the equation as shown below:
\[\begin{align}
& \text{Interest amount}=\text{Total of Monthly payments}-\text{Amount of mortgage} \\
& =\left( \$1,277\times360\right)-\$192,000\\&=\$267,720\end{align}\]
Hence, the total cost of interest amount is \[\$267,720\]
