MATH 105 Final Exam

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Mathematics

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Jun 22, 2024

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MATH 105 Final Exam, Summer 2021 • A score of 100% on the final will earn you 12 points toward your final grade, 90% = 10.8 pts, 80% = 9.6 pts, 70% = 8.4 pts, 60% = 7.2 points, 50% = 6 pts, etc. • The exam has 3 Parts. • The exam is available on the first day of week 8. • You may take as long as you like on this exam, but you must complete and submit to your LEO classroom assignment folder by 11:59 pm on the last day of class. • The online text and the ALEKS lesson pages are a resource as you work on these problems. • Please submit your work in the LEO assignment folder as ONE single file o typed and saved as a single file and attached OR o neatly handwritten, scanned, and saved as a single file and attached . Be sure that the pages are right- side-up and in order • You MUST show all of your work to receive any credit. If you have questions about showing work, please ask. Your work must be shown in a very neat presentation that is easily followed. • The Final Exam is open book and open notes. You may refer to your textbook, notes, and online classroom materials, but you may not consult with anyone in person or online . You may not use any online service to solve any of the problems. The following statement must be signed and dated: I have completed this Final Exam myself, working independently and not consulting with anyone except the instructor nor with any online source except ALEKS. I have neither given nor received help on this exam. Name Date 7/12/2021

Part 1 (40 points) You are planning to purchase a house that will require a mortgage of $400,000. You find 2 mortgage offers both at the same rate of 2.75%. One is a 30-year mortgage and the other is a 20-year mortgage. 1. (10 pts) You know, without any computation, that the 30-year mortgage will have lower monthly payments than the 20-year mortgage since the rates are the same. A friend advised that before taking the 30-year mortgage offer, you do some mathematical calculations to see if your budget can handle the extra amount of monthly payment for the 20-year mortgage. What is the difference in the monthly payment? Be sure to show all of your work. 30-year mortgage P = $400,000 r = 0.0275 n = 12 t = 30 R = P(r/n) 1 – (1 + r/n)-nt R = 400,000(0.0275/12) 1 – (1 + 0.0275/12) -30(12) R = 916.666 1-(1.00229) -360 R = 916.666 0.56108850871 R = 1632.96 20-year mortgage P = $400,000 r = 0.0275 n = 12 t = 20

R = P(r/n) 1 – (1 + r/n)-nt R = 400,000(0.0275/12) 1 – (1 + 0.0275/12) -20(12) R = 916.666 1-(1.00229) -240 R = 916.666 0.42245658797 R = 2169.83 Answer: $536.87 ($2169.83: 20yr mortgage - $1632.96: 30yr mortgage) 2. (10 pts) You ask your friend what advantage there is to be paying more per month on the 20-year mortgage. Your friend replies that it is all about total interest. What is the difference between the total interest paid over the term of the 30 year and 20-year mortgage? Be sure to show all of your work. 30-year mortgage Monthly payment = $1632.96 Total number of payments = 360 Total cost: $1632.96 X 360 = $587,865.60 Purchase Price = $400,000 Total interest: (Total Cost) $587,865.60 – (Purchase Price) $400,000 = $187,865.60 (Total Interest) 20-year mortgage Monthly payment = $2169.83 Total number of payments = 240 Total cost: $2169.83 X 240 = $520,759.20 Purchase Price = $400,000 Total interest: (Total Cost) $520,759.20 – (Purchase Price) $400,000 = $120,759.20 (Total Interest)

Answer: Difference in interest: (30-yr) $187,865.60 – (20-yr) $120,759.20 = $67,106.40 3. (10 pts) After you purchase the house, you decide to do some remodeling in the kitchen. You ask your parents if they would lend you money, but you insist on paying them interest. The agreement is that they will lend you $6000.00 at a simple interest rate of 3% per year. Once the interest amounts to $300, you agree to pay them back the $6000 plus the $300 interest. After how many months will you have to pay them back? Be sure to show all of your work. I = $300, P = $6000, r = 3% (0.03), t = ? I = Prt 300 = (6000)(0.03)t Divide both sides by (6000)(0.03) 300 = (6000)(0.03)t (6000)(0.03) = (6000)(0.03)t 1.666 = t Answer: 1.666t = 1 year 9 months = 21 months total 4. (10 pts) Suppose that the $6000.00 was invested in a savings account that paid 2.5% interest compounded quarterly . How much interest would be earned after 3 years? Be sure to show all of your work. P = $6000, r = 2.5% (0.025), t = 3, n = 4 A = P(1 + r/n) nt A = 6000(1 + 0.025/4) (4)3 A = 6000(1.00625) 12 A = 6465.795 Answer: Interest = $6465.80 - $6000 = $465.80

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