MM255 PROJECT 6
MM255 PROJECT 6
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Date Created: 11/14/15
Unit 6 Compound Interest Instructor Graded Project You must show your work on all problems You may type your answer right into this document Total points for project 45 points Projects must be submitted as a Microsoft Word document and uploaded to the Dropbox for Unit 6 All Projects are due by Tuesday at 1159 PM ET of the assigned Unit NOTE Project problems should not be posted to the Discussion threads Questions on the project problems should be addressed to the instructor by sending an email or by attending office hours Part Basic Computations 1 A Find the future value on 6000 in three years if the interest is compounded semiannually at 12 5 points Answer 851111 FV PV1rnquotnT 600010122quot23 851111 B What is the compound interest earned 5 points Answer 251111 8511116000251111 2 You have 12000 that you plan to invest in a compoundinterest bearing interest Your investment agent advises you that you can invest the 12000 at 8 compounded quarterly for three years or you can invest it at 8 14 compounded annually for three years Which investment should you choose to receive the most interest Show your work for calculating the interest for both options 10 points Answer compounded quarterly Interest 1200010084quot34 12000 321890 compounded annually 12000100825quot312000 322176 See the second option is giving more interest Should choose the 8 14 compounded annually Part II Case Study Willie owns and manages a number of realestate rental properties in town and enjoys being his own boss At 46 years old Willie gures he would like to retire after working for 10 more years so he is starting to think about investing for the future His latest investments have been successful after selling a fourunit apartment building and a town house Willie has 300000 in the bank and is debtfree With only 10 years before retirement Willie wants to make solid nancial decisions that will limit his risk exposure An attractive property has come on the market this week a pair of townhouses with a great view The rental units are in good condition and would need only some minor repairs in order to get them into shape for rental They are in a good location for vacationers and summer rentals The price tag for the two townhouses totals 225000 well within his range He gures he can invest the remaining 75000 and between the two hopes to have 600000 on which to retire by age 56 1 Willie knows that real estate in this general location appreciates by about 5 a year Assuming that this trend continues what will be the future value of the 225000 townhouses in 10 years 5 points Answer 36650129 Future value 2250001 005quot10 225000105quot10 22500016289 36650129 2 Willie s local bank offers a 2year certi cate of deposit CD that pays 5 compounded quarterly A competing bank in town also offers a 2 year CD that pays 5 but the interest is componded daily If Willie invests the 75000 how much more money will he get from the second bank after two years due to the daily compounding assume exact time is used 5 points Answer The future value of the 75000 at 5 compounded quarterly is FV 750001 0054quot4 2 7500010125quot8 8283646 The future value of 75000 at 5 compounded daily using exact time meaning 265 days in a year would be FV 750001 005365quot365 2 7500010001370quot730 8288725 The difference in the interest earned is 8288725 8283646 5079 Willie would earn an additional 5079 by investing in the CD with daily compounding After purchasing the townhouses Willie receives an assessment from the town for 17500 due in 2 years to pay for road repairs and new sewer hookups for the properties How much would he need to invest today in a CD paying 5 compounded semiannually to fully pay the assessment in 2 years 5 points Answer To have 17500 in 2 years at 5 compounded semiannually Willie must invest Future value Prevent vaue1 annual interest rate number of periods per yearquotnumber of years number of periods per year The future value here is the 17500 that would be due at the end of 2 years The annual interest rate is 5 Expressed as a decimal it is 005 The number of periods per year is 2 because the interest is paid semi annuaHy The number of years is 2 Substituting these values and solving for the present value gives 17500 PV1 0052quot22 17500 PV1 0025quot4 PV 17500 1025quot4 PV 1585414 Willie would need to invest 1585414 today A friend of Willie s is a real estate developer and needs to borrow 75000 to nish a development project He is desparate for cash and offers Willie 18 compounded monthly for 2 12 years Given that he can invest the money at a sure 5 with the bank does this loan meet with Willie s goals for low risk investment Research some of the risks associated with this type of loan Can you think of any ways to reduce the risk 10 points Requirements Write your essay in this document do not save it in a separate le You must clearly state your position with wellstructured paragraphs using proper grammar spelling and sentence structure This is not an opinion question you must offer evidence to support your position using properlycited sources Your answer must be between 150250 words about 1 page of text You must cite at least one source book website periodical using APA format Do not use unreliable sources such as Wikipedia and Yahoo Answers Answer Case1 Willie lends 75000 to his real estate friend at 18 compounded monthly for 25 years PV 75000 r 18l2 15 n 25l2 30 FV PVlrr1 FV 75000ll530 117231 At the end of 25 years Willie s money will grow to 117231 Case2 Willie keeps money in bank at 5 Assuming interest is compounded annually PV 75000 r 5 n 25 FV 75000l5quot25 84729 So in this case Willie s money will grow to 84729 at the end of 25 years If both propositions were bearing same level of risk Willie would have chosen to lend to his real estate friend as that option would generate much higher return But risk associated with lending to real estate friend is much higher than risk associated with keeping the money in bank There is very low probability of bank defaulting on repaying the money But if Willie lends to real estate friend he is exposed to default risk as well as liquidity risk His real estate friend may not be able to pay interest on time He may not even repay the loan So default risk is very high If Willie wants money before 25 years his friend may not repay the loan Therefore liquidity risk is also high Risk of lending to real estate developer depends on legal standing of the lender Lea er al 1997 Willie can lower default risk if his real estate friend mortgages property against the loan Willie can ask the friend to enter in a contract with Willie that gives Willie right to foreclose on defaulted loan This way Willie can reduce default risk To reduce liquidity risk Willie can also put a clause in contract that gives him right to ask for loan before maturity by paying some penalty References Lea M j Dubel A Laszekj 1997 The risks ofcommercia real estate lending East European Regional Urban Sector Assistance Project Project 1800034 Retrieved from httppdfusaiddovDdfdocsPNACI140pdf Students in MM255 may submit their projects to the Math Center for review Tutors will not grade or correct the project but they will provide guidance for improvement Students should submit assignments early enough to receive feedback and make corrections before the project due date 24 hour turnaround times MondayThursday and 48 hour turnaround times on weekends are typical Email projects to kumckaplanedu Please put quotproject reviewquot in the subject line of the message
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