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 34P
To determine

(a)

If the house is affordable or not.

Expert Solution
Check Mark

Answer to Problem 34P

The house is affordable.

Explanation of Solution

Given:

The purchase price of the house is $170000.

The down payment required is 5%.

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

The bank is offering 30 year mortgage.

Interest on mortgage is 5.35% compounded annually.

The annual after tax income is $85000.

Other debts are $850 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, monthly mortgage is M, 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=5%×$170000=5100×$170000=$8500

Calculate the loan for the house.

loan(L)=$170000$8500=$161500

Calculate the insurance.

Insurance =1%×$161500=1100×$161500=$1615

Calculate the monthly insurance.

I=Insurance12=$161512=$134.58

Calculate the monthly interest rate.

i=5.35%12=0.4458%

Calculate the monthly mortgage.

Substitute 0.004458 for i, (30×12months=360) for n and $161500 for L in Equation (I).

M=$161500×[0.004458 ( 1+0.004458 ) 360][ ( 1+0.004458 ) 3601]=$161500×[0.004458×4.96][4.961]=$161500×0.02213.96=$901.7

Calculate the monthly income.

I=$8500012=$7083.33

Calculate the debt to income ratio.

Substitute $901.7 for M, $850 for D, $134.58 for I and $7083.33 for I in Equation (II).

Ratio=$901.7+$850+$134.58$7083.33=$1886.28$7083.33=0.266.

Conclusion:

The house is affordable because the calculated debt to income ratio of 0.266 which is less 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 34P

The total payment after 30 years is $333112.

Explanation of Solution

Write the expression for total payment.

P=(M×n)+(downpayment) ....... (II)

Here, the total payment is P.

Calculations:

Calculate the total payment after 30 years.

Substitute (30×12months=360) for n, $901.7 for M and $8500 for down payment in Equation (II).

P=($901.7×360)+$8500=$324612+$8500=$333112.

Conclusion:

The total payment after 30 years is $333112.

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