Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
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Chapter 12A, Problem 35P
To determine

(a)

If the house is affordable or not.

Expert Solution
Check Mark

Answer to Problem 35P

The house is not affordable.

Explanation of Solution

Given:

The purchase price of the house is $260000.

The down payment required is 10%.

The insurance is of 1% of the loan amount each year.

The bank is offering 30 year mortgage.

Interest on the mortgage is 5.15% compounded annually.

The annual after tax income is $55000.

Other debts of $650 per month.

The maximum debt to income ratio is 43%.

Concept used:

Write the expression for monthly mortgage.

M=L[i( 1+i)n][( 1+i)n1] ....... (I)

Here, loan is L, per payment interest is i and number of payment is n.

Write the expression for debt to income ratio.

Ratio=M+D+II ....... (II)

Here, monthly income is I, monthly debt is D and monthly insurance is I.

Calculations:

Calculate the down payment for the house.

Down payment=10%×$260000=10100×$260000=$26000

Calculate the loan for the house.

loan(L)=$260000$26000=$234000

Calculate the insurance.

Insurance =1%×$234000=1100×$234000=$2340

Calculate the monthly insurance.

I=Insurance12=$234012=$195

Calculate the monthly interest rate.

i=5.15%12=0.429%

Calculate the monthly mortgage.

Substitute 0.00429 for i, (30×12months=360) for n, and $234000 for L in Equation (I).

M=$234000×[0.00429 ( 1+0.00429 ) 360][ ( 1+0.00429 ) 3601]=$234000×[0.00429×4.672][4.6721]=$234000×0.023.672=$1227.37

Calculate the monthly income.

I=$5500012=$4583.33

Calculate the debt to income ratio.

Substitute $1227.37 for M, $650 for D, $195 for I and $4583.33 for I in Equation (II)

Ratio=$1227.37+$650+$195$4583.33=$2072.37$4583.33=0.452.

Conclusion:

The house is not affordable as the calculated debt to income ratio of 0.452 is more than the maximum debt to income ratio of 0.43.

To determine

(b)

The total payment paid after 30 years.

Expert Solution
Check Mark

Answer to Problem 35P

The total payment after 30 years is $538053.2.

Explanation of Solution

Concept used:

Write the expression for total payment.

P=(M×n)+(I×30)+down payment ....... (II)

Calculations:

Calculate the total payment after 30 years.

Substitute (30×12months=360) for n, and $1227.37 for M, $2340 for I and $26000 for down payment in Equation (II).

P=($1227.37×360)+($2340×30)+$26000=$441853.2+$70200+$26000=$538053.2.

Conclusion:

Thus, the total payment after 30 years is $538053.2.

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