Chapter 8, Problem 7DC2

Summary Introduction

To discuss:

Monthly local estate tax and insurance, monthly principal and interest for 15, 20 and 30 years loan and whether S can take these loan or not.

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

Monthly local real estate tax:

Given,

Real estate tax rate is 0.91%.

Number of months is 12.

Assessed value is $180,000.

Formula to calculate monthly local real estate tax,

$\text{Monthly real estate tax}=\frac{\text{Real estate tax rate}}{\text{Number of months}}\times \text{Assessed value}$

Substitute, 0.91% for real estate tax rate, 12 for number of months and $180,000 for assessed value in the above formula.

$\begin{array}{c}\text{Monthly real estate tax}=\frac{0.91}{100\times 12}\times \$180,000\\ =\$136.50\end{array}$

Monthly real estate tax is $136.50.

Homeowner’s insurance:

Given,

Total homeowner’s insurance is $275.

Number of months is 12.

Formula to calculate monthly homeowner’s insurance,

$\text{Monthly homeowner's insurance}=\frac{\text{Total homeowner's insurance}}{\text{Number of months}}$

Substitute, $275 for total homeowner’s insurance and 12 for number of months in the above formula.

$\begin{array}{c}\text{Monthly homeowner's insurance}=\frac{\text{\$275}}{\text{12}}\\ =\$22.91\end{array}$

Monthly homeowner’s insurance is $22.91.

Loan amount:

Given,

House price is $180,000.

Down payment is $36,000.

Formula to calculate loan amount,

$\text{Loan amount}=\text{House price}-\text{Down payment}$

Substitute $180,000 for house price and $36,000 for down payment in the above formula.

$\begin{array}{c}\text{Loan amount}=\text{\$180,000}-\text{\$36,000}\\ =\$144,000\end{array}$

Loan amount is $144,000.

Principal and interest:

The formula to calculate the amount of monthly payment is,

$PMT=PV\times \left(\frac{\frac{i}{m}}{1-{\left(1+\frac{i}{m}\right)}^{-n\times m}}\right)\mathrm{ }\mathrm{(1)}$

Where,

• PMT is amount of monthly payment.
• PV is the present value.
• i is the rate of interest.
• n is the number of years.
• m is the number of payment in a year.

For 15 years

Given,

PV is $144,000.

i is 5.25%.

n is 15 years.

m is 12

Substitute $144,000 for PV, 5.25% for i, 15 for n and12 for m in the above equation (1).

$\begin{array}{c}PMT=\$144,000\times \left(\frac{\frac{0.0525}{12}}{1-{\left(1+\frac{0.0525}{12}\right)}^{-15\times 12}}\right)\\ =\$144,000\times \frac{0.0043}{1-0.4557}\\ =\$1,157.58\end{array}$

Total principal and interest is $1,157.58.

For 20 years

Given,

PV is $144,000.

i is 5.25%.

n is 20 years.

m is 12.

Substitute $144,000 for PV, 5.25% for i, 20 for n and12 for m in the above equation (1).

$\begin{array}{c}PMT=\$144,000\times \left(\frac{\frac{0.0525}{12}}{1-{\left(1+\frac{0.0525}{12}\right)}^{-20\times 12}}\right)\\ =\$144,000\times \frac{0.0043}{1-0.3507}\\ =\$970.34\end{array}$

Total principal and interest is $970.34.

For 30 years

Given,

PV is $144,000.

i is 5.25%.

n is 30 years.

m is 12.

Substitute $144,000 for PV, 5.25% for i, 30 for n and12 for m in the above equation (1).

$\begin{array}{c}PMT=\$144,000\times \left(\frac{\frac{0.0525}{12}}{1-{\left(1+\frac{0.0525}{12}\right)}^{-30\times 12}}\right)\\ =\$144,000\times \frac{0.0043}{1-0.2077}\\ =\$795.17\end{array}$

Total principal and interest is $795.17

Maximum amount that can be used for home payment:

Given,

Amount that can be use for payment of PITI is $1,470.

Monthly insurance is $22.91.

Formula to calculate maximum amount that can be use for home payment,

$\text{Maximum amount}=\left(\begin{array}{l}\text{Amount that can be use for payment of PITI}\\ -\text{Taxes and insurnace}\end{array}\right)$

Substitute, $1470 for amount that can be used as PITI and $22.91 for monthly insurance in the above formula.

$\begin{array}{c}\text{Maximum amount}=\$1,470-\$22.91\\ =\$1,447.09\end{array}$

Maximum amount is $1,447.09.

Working notes:

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

$\begin{array}{c}\text{Amount that be used for payment of PITI}=\frac{\text{Pretax income}}{\text{Number of months in a year}}\times \text{Rate}\\ =\frac{\$63,000}{12}\times \frac{28}{100}\\ =\$1,470\end{array}$

Calculation for monthly insurance,

$\begin{array}{c}\text{Monthly insurance}=\frac{\text{Total insurance}}{\text{Number of months}}\\ =\frac{\$275}{12}\\ =\$22.91\end{array}$

Conclusion

Hence, S can take loan for 15, 20 and 30 years as he seems fit because he has $1,447.09 for home payment and payment in those three options is lower than that.