Chapter ISG, Problem 7.7.1P

a.

To determine

To Find: The total amount to be paid by Mr. and Mrs. Ramirej after 15 Years.

Answer to Problem 7.7.1P

The total amount paid after 15 years $\mathrm{\$}191700$ .

Explanation of Solution

Given Information:

The price of house $\mathrm{P}=\mathrm{\$}180000$

The monthly payment $\mathrm{i}=\mathrm{\$}1065$

The percentage down payment $\mathrm{d}=20\mathrm{\%}$

Calculation:

Calculate the amount paid as down payment.

  $\begin{array}{c}{\mathrm{P}}_{\text{dp}}=0.2\times \mathrm{\$}180000\\ =\mathrm{\$}36000\end{array}$

Calculate the amount left for the interest for the 15 years.

  $\begin{array}{c}{\mathrm{P}}_{\mathrm{i}}=\mathrm{P}-{\mathrm{P}}_{\text{dp}}\\ =\mathrm{\$}180000-\mathrm{\$}36000\\ =\mathrm{\$}144000\end{array}$

Calculate the total amount paid after 15 years.

  $\begin{array}{c}\mathrm{T}=\left(\mathrm{i}\times \mathrm{t}\right)\\ =\left(1065\times 12\times 15\right)\\ =\mathrm{\$}191700\end{array}$

Hence, the total amount paid after 15 years $\mathrm{\$}191700$ .

b.

To determine

To Write: The expression to show the future value of house as a function of time and calculate the future value.

Answer to Problem 7.7.1P

The expression for the future value of house is $\mathrm{F}\mathrm{V}=\mathrm{P}{\left(1+{\mathrm{r}}_{\text{annual}}\right)}^{\mathrm{n}}$ and the future value of the house after $\mathrm{\$}431380.47$ .

Explanation of Solution

Given Information:

The rate of increase of value of house every year ${\mathrm{r}}_{\text{increase}}=6\mathrm{\%}$

Calculation:

Write the expression for the future value as function of t.

  $\mathrm{F}\mathrm{V}=\mathrm{P}{\left(1+{\mathrm{r}}_{\text{increase}}\right)}^{\mathrm{n}}$

Substitute the values in the above expression

  $\begin{array}{c}\mathrm{F}\mathrm{V}=180000{\left(1+0.06\right)}^{15}\\ =\mathrm{\$}431380.47\end{array}$

Thus, the future value of the house after $\mathrm{\$}431380.47$ .

c.

To determine

To Find: The return on the investment.

Answer to Problem 7.7.1P

The returns of the investment is $\mathrm{\$}203680.47$ .

Explanation of Solution

Given Information:

The future value of the house after 15 years is $\mathrm{F}\mathrm{V}=\mathrm{\$}431380.47$

The total amount paid after 15 years is $\mathrm{\$}191700$ .

Calculation:

Calculate the amount of returns of investments.

  $\begin{array}{c}\text{Returns}=\mathrm{F}\mathrm{V}-\left(\mathrm{T}+{\mathrm{P}}_{\text{dp}}\right)\\ =\mathrm{\$}431380.47-\mathrm{\$}\left(191700+36000\right)\\ =\mathrm{\$}203680.474\end{array}$

Thus, the returns of the investment is $\mathrm{\$}203680.47$ .