Chapter 8, Problem CC.27Q

Summary Introduction

To discuss:

Total cost of home mortgage and amount of interest in it.

Introduction:

PITI is a short form for principal, interest, tax and insurance payments. Generally, buyer has to pay property tax and insurance along with interest and principal amount of the home purchase. PITI limit is 28% of one’s pretax monthly income.

Explanation of Solution

According to 28%:

Total interest paid:

Given,

Total repayment is $644,400.

PVis $374,935.62.

Formula to calculate total interest is,

$\text{Total interest}=\text{Total repayment}-PV$

Where,

• PVis present value.

Substitute, $644,400 for total repayment and $374,935.62 for PVin the above formula.

$\begin{array}{c}\text{Total interest}=\text{\$644,400}-\$374,935.62\\ =\text{\$269,464}\text{.38}\end{array}$

Total interest paid is $269,464.38.

Working notes:

Calculation for amount that can be used for payment of PITI,

$\begin{array}{c}\text{Amount that be used for payment of PITI}=\text{Income}\times \text{Rate}\\ =\$7,000\times \frac{28}{100}\\ =\$1,960\end{array}$

Calculation for PMT,

$\begin{array}{c}PMT=\left(\begin{array}{l}\text{Amount that can be use for payment of PITI}\\ -\text{Taxes and insurnace}\end{array}\right)\\ =\$1,960-\$170\\ =\$1,790\end{array}$

Calculation for PV,

$\begin{array}{c}PV=PMT\times \left(\frac{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}{\frac{i}{m}}\right)\\ =\$1,790\times \left(\frac{1-{\left(1+\frac{0.04}{12}\right)}^{-30\times 12}}{\frac{0.04}{12}}\right)\\ =\$1,790\times \frac{1-0.3017}{0.0033}\\ =\$374,935.62\end{array}$

Calculation for total repayment,

$\begin{array}{c}\text{Total repayment}=\text{Monthly payment}\times \text{Number of payment}\\ =\$1,790\times 360\\ =\$644,400\end{array}$

According to 36%:

Total interest paid:

Given,

Total repayment is $518,040.

PVis $301,414.73.

Formula to calculate total interest is,

$\text{Total interest}=\text{Total repayment}-PV$

Where,

• PVis present value.

Substitute, $518,040 for total repayment and $301,414.73 for PVin the above formula.

$\begin{array}{c}\text{Total interest}=\$518,040-\$301,414.73\\ =\$\text{216,625}\text{.27}\end{array}$

Total interest paid is $216,625.27.

Working notes:

Calculation for amount that can be used for payment of PITI,

$\begin{array}{c}\text{Amount that be used for payment of PITI}=\text{Income}\times \text{Rate}\\ =\$7,000\times \frac{36}{100}\\ =\$2,520\end{array}$

Calculation for PMT,

$\begin{array}{c}PMT=\left(\begin{array}{l}\text{Amount that can be use for payment of PITI}\\ -\text{Taxes and insurnace}-\text{Total debt}\end{array}\right)\\ =\$2,520-\$170-\$911\\ =\$1,439\end{array}$

Calculation for PV,

$\begin{array}{c}PV=PMT\times \left(\frac{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}{\frac{i}{m}}\right)\\ =\$1,439\times \left(\frac{1-{\left(1+\frac{0.04}{12}\right)}^{-30\times 12}}{\frac{0.04}{12}}\right)\\ =\$1,439\times \frac{1-0.3017}{0.0033}\\ =\$301,414.73\end{array}$

Calculation for total repayment,

$\begin{array}{c}\text{Total repayment}=\text{Monthly payment}\times \text{Number of payment}\\ =\$1,439\times 360\\ =\$518,040\end{array}$

Conclusion

Hence, Total interest according to 28% and 36% is $269,464.38 and $216,625.27 respectively.