Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
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Chapter 4, Problem 1CS
To determine

Total worth of plan B.

Expert Solution & Answer
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Explanation of Solution

Time period is 15 years. Down payment (DP) is 10%. Fixed rate (i) is 5%. Price of house (Pr) is $330,000. Fee (UF) is $3,000.

Total payment (TP) can be calculated as follows:

Total payment=(Pr×DP)+UF=(330,000×0.1)+3,000=33,000+3,000=36,000

Total payment is $36,000.

Loan amount (LM) can be calculated as follows:

Loan payment=Pr(Pr×DP)=330,000(330,000×0.1)=330,00033,000=297,000

Loan payment is $297,000.

Tax and insurance (TI) is $500 per month. Interest rate per month (im) is 0.4167% (512). Time period (n) is 180 (15×12) months. Equivalent annual value of monthly payment can be calculated as follows:

A=LM(im(1+im)n(1+im)n1)+TI=297,000(0.004167(1+0.004167)180(1+0.004167)1801)+500=297,000(0.004167(2.1138302)2.1138302)+500=297,000(0.00880831.1138302)+500=297,000(0.00790081)+500=2,346.54+500=2,846.54

Equivalent monthly loan repayment is $2,847 per month.

The remaining money after monthly payment and down payment (ia) is deducted, earns 0.5% interest rate per month. Available amount (AV) is $40,000. Time period (n1) is 120 (10×12) months.  Future worth of available amount (FA) can be calculated as follows:

FA=(AVTP)(1+ia)n1=(40,00036,000)(1+0.005)120=(4,000)(1.819397)=7,277.59

Future value of remaining available amount is $7,278.

The person can afford the monthly payment (MP) of $2,850. The future value of remaining monthly available amount (FM) can be calculated as follows:

FM=(MPA)(1+ia)n1=(2,8502,847)(1+0.005)120=(3)(1.819397)=5.46

The future value of remaining monthly available amount is $5.

Future value of loan balance (FB) can be calculated as follows:

FB=LM(1+im)n1A((1+im)n1im)=297,000(1+0.004167)1202,847((1+0.004167)12010.004167)=297,000(1.647075)2,847(1.64707510.004167)=297,000(1.647075)2,847(0.6470750.004167)=297,000(1.647075)2,847(155.285577)=489,181.275442,098.038=47,083.24

Future value of loan balance is $47,083.

Selling price (SP) is $363,000. Increase in the future value of house (FH) can be calculated as follows:

FH=SPFB=363,00047,083=315,917

Future value of house is $315,917.

Total future worth (TFW) of plan B can be calculated as follows:

TFW=FA+FM+FH=7,278+5+315,917=323,200

Total future worth of plan B is $323,200. Total future worth of plan B is greater than plan A. Thus, select plan B.

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Engineering Economy

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