Math Self-Assessmet This self-assessmet tool has bee created to assist studets review their ow math kowledge ad idetify areas where they may require more assistace. We hope that studets will complete this assessmet prior to startig the course, so that they may direct the appropriate attetio to problematic areas before they ecouter major difficulties with the course. Because the cocepts covered i this self-assessmet are from earlier courses i the program, studets are expected to have mastered them before carryig o to the curret course ad should ot rely o their course tutor for assistace with difficulties i these areas. The self-assessmet will test the followig six major areas, relevat to studies i the Real Estate Divisio's credit-based courses: I. Basic Math Calculatios II. Iterest Rate Coversios III. Basic Mortgage Calculatios IV. Advaced Mortgage Calculatios V. Ivestmet Aalysis VI. Statistics The cocepts covered will focus o the use of the HP10BII calculator. If you have difficulties with this calculator, you should review the Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios documet, foud uder "Pre-Readig" o the Course Resources webpage. As well, you may wish to cosider the computer based traiig tool discussed below. The UBC Real Estate Divisio, i cojuctio with Hewlett Packard, has developed a computer based traiig (CBT) tool for the HP10BII calculator, targeted at studets who require assistace with masterig the key strokes o the calculator. This iteractive traiig tool shows the steps o the calculator that are required to solve various real estate fiace problems. The CBT tool ca be accessed at http://www.hp.com/calculators/traiig/cbt/hp10bii_realestate.html. Please ote that this will lik to the Hewlett Packard website ad i order to view the applicatio, users must have Macromedia Shockwave Flash Player istalled. To dowload this free plug-i, visit the Macromedia website at http://sdc.shockwave.com/shockwave/dowload/dowload.cgi? ad follow the o-scree istructios. Math Self-Assessmet Istructios 1. Complete this multiple choice test usig oly your calculator ad/or free-had calculatios where ecessary. Do NOT use ay other material, except for the formulae provided at the ed of this documet.. Select oly oe aswer for each questio. 3. Whe complete, calculate your score out of a possible 30 poits, scorig oe poit for each questio aswered correctly. 4. Use the followig Guide to assess your level of kowledge: Score: 6-30 You are proficiet i the math required for your course. 1-5 You may require some assistace. Please review the questios you aswered icorrectly ad, if ecessary, referece the materials outlied at the ed of each sectio as a aid. 16-0 Review is ecessary. To avoid difficulties i your course, you should use the recommeded materials to improve your math skills before commecig coursework. 0-15 Your math skills are iadequate to begi course study. Before begiig your course, you must review each sectio covered i this self-test i detail, esurig you have developed a greater level of proficiecy.
Real Estate Divisio Math Self-Assessmet Page 1 I. Basic Calculatios The followig sectio will test your kowledge of basic arithmetic, usig the HP10BII Calculator. These questios are iteded as a itroductio to test your familiarity with the basic operatios of this calculator. 1. Solve 1 x 5-1 = (1) 300 () 50 (3) 88 (4) 156. Solve 5% x $837 = (1) $418.50 () $41.85 (3) $167.40 (4) $1,674.00 3. Solve.34304 3 = (1) 1.494734387 () 0.447581413 (3) 11.157988703 (4) 6.0604394468 4. Solve (1 + 0.105) - 1 = (1) 1.55065% () 1.05065% (3) 0.5% (4) 10.5% 5. Solve -5 x 6 + 4 x 13 = (1) 8 () 1,560 (3) -1,560 (4) If you experieced difficulty with Questio 1, you should review: order of operatios. If you experieced difficulty with Questio, you should review: coversio of percetage. If you experieced difficulty with Questio 3, you should review: expoets. If you experieced difficulty with Questio 4, you should review: expoets ad order of operatios. If you experieced difficulty with Questio 5, you should review: order of operatios, egative sigs, ad memory keys. For additioal help o the topics above, you may wish to review the followig materials, foud uder Pre- Readig o your course s Olie Readigs webpage: Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios, with a focus o pages -1. Math Review Kit (Provided with permissio from CGA Caada). As well, you may wish to review the HP10BII CBT tool. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page II. Iterest Rate Coversios The followig sectio will test your kowledge o the basic coversio of omial iterest rates to other equivalet rates. Studets are expected to be able to covert omial iterest rates to equivalet aual rates, equivalet omial rates, ad equivalet periodic iterest rates. 6. Calculate the effective aual rate of iterest which is equivalet to j = 1%. (1) 1.30403010% () 1.68503013% (3) 1% (4) 1.36% 7. Which of the followig iterest rates is NOT equivalet to j = 11.5%? (1) j = 11.193556791% 5 () i =.8348190060% q (3) i = 5.75% sa (4) j = 11.9104496% 1 8. Which of the followig iterest rates is equivalet to j = 10%? 365 (1) j = 10.03909374% 1 () j = 10.14643974% 4 (3) j = 10% 5 (4) j = 10.5155781616% 9. Which of the followig mothly periodic rates is equivalet to j = 10%? 1 (1) 1% () 0.833333333% (3) 0.854166667% (4) 0.87608895% 10. Which of the followig periodic iterest rates is equivalet to j = 14%? (1) i = 1.5346633453% mo () i = 3.4408043788% q (3) = 7.45% isa (4) i = 0.04987989797% d For additioal help o the topics above, you may wish to review the followig materials: Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios, with a focus o pages 13-15. BUSI 11 textbook Foudatios of Real Estate Fiacig, with a focus o Chapter. As well, you may wish to review the HP10BII CBT tool, specifically the Equivalet Iterest Rates i the Itroductio to Mortgage Fiace Sectio. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 3 III. Basic Mortgage Calculatios The followig sectio will test your ability to perform basic mortgage calculatios whe solvig for the variables: preset value, future value, iterest rate, amortizatio period, or paymet. Uless otherwise stated, please assume that all paymets are rouded up the ext higher cet. 11. A ivestor borrows $140,000 at % per compoudig period for six periods. How much will be owig at the ed of the term if the iterest is accruig? (1) $140,000.00 () $170,800.00 (3) $ 36,35.6 (4) $461,6.55 1. A borrower wishes to make paymets of o more tha $500 per moth for 360 moths. If iterest rates are curretly 10.5% per aum, compouded semi-aually, what is the maximum amout that should be let? (1) $55,500.00 () $54,660.38 (3) $55,670.60 (4) $56,675.77 13. A vedor is willig to sell his house for $95,000. He demads 36 mothly paymets, ad paymet of th the outstadig balace i the amout of $80,000 with the 36 paymet. He wishes to ear a effective aual rate of 1% o his moey. What is the required mothly paymet? (1) $1,98. () $1,5.94 (3) $1,76.85 (4) $ 493.84 14. Cosider a $75,000 loa requirig a 5-year amortizatio period ad mothly paymets. Assumig that the mothly paymets o the loa are $750, what is the iterest rate, expressed as a j? (1) 11.54353584% () 11.8754171033% (3) 11.74040198% (4) 11.679076807% th 15. Calculate the outstadig balace o the followig mortgage immediately after the 60 mothly paymet is made. Paymets are rouded up to the ext higher cet. Face Value: $55,000 Iterest Rate: 15% per aum, compouded semi-aually, ot i advace Amortizatio Period: 5 years (1) $55,387.48 () $53,44.16 (3) $39,510.01 (4) $53,386.61 For additioal help o the topics above, you may wish to review the followig materials: Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios, with a focus o pages 16-37. BUSI 11 textbook Foudatios of Real Estate Fiacig, with a focus o Chapters 4-6. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 4 As well, you may wish to review HP10BII CBT tool, specifically the Itroductio to Mortgage Fiace sectio. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 5 IV. Advaced Mortgage Calculatios The followig sectio will test your kowledge o boused mortgages, the determiatio of equivalet paymets, market value of offers, mortgage assumptio, ad iterest adjustmet. 16. A loa cotract was writte with a face value of $50,000 at j = 10.75%, with a 0-year amortizatio ad a five-year term. Paymets were to be made mothly i the amout of $499.76 ad the outstadig balace at the ed of the term was $45,167.50. A brokerage fee of $,000 was deducted from the face value, so the fuds actually advaced to the borrower were $48,000. What is the effective aual rate of iterest o the fuds advaced? (1) 1.57093717% () 11.0389057614% (3) 11.6180341755% (4) 10.516863947% 17. A borrower wishes to alter the frequecy of paymets o his mortgage. Curretly, he makes mothly paymets of $675.75, based o a iterest rate of j = 15%. How much would a equivalet semiaual paymet be? (1) $4,054.51 () $4,16.97 (3) $4,179.43 (4) Impossible to calculate from the iformatio give. 18. Gio wats to buy Pavel s luxurious masio i the British Properties. Oe year ago, Pavel purchased the $,500,000 property with a cash dow paymet of $750,000 ad private fiacig. The remaiig portio of the purchase price was fiaced by Pavel s older brother, Valeri, who let the moey to Pavel at a rate of j = 1.5%, fully amortized over 5 years, with mothly paymets. Gio is offerig Pavel a dow paymet of $800,000 ad Gio will assume the existig mortgage which has 4 years remaiig i the term. The curret market rate of iterest for similar mortgages is j = 13.5%. Igore the effect of roudig o the fial paymet of the mortgage. What is the market value of Gio s offer? (1) $,431,71.18 () $,440,805.85 (3) $1,640,805.85 (4) $,68,945.70 19. Mary ad Herbert have received a offer of $0,000 o their house i Buraby. It is comprised of a cash dow paymet of $70,000, ad a vedor supplied mortgage of $150,000 at 10% per aum, compoudig semi-aually, to be amortized over 0 years with mothly paymets. There is a 5 year term. Market rates of iterest o equivalet mortgages are curretly 13% per aum, compoudig aually. The market value of the offer is: (1) $ 06,697.76 () $ 139,007.65 (3) $ 197,345.7 (4) $ 03,137.71 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 6 0. Marsha Clerk has arraged for a $5,000 mortgage loa with the Cochrae Credit Uio. The mortgage loa was writte at a iterest rate of 7.5% per aum, compouded semi-aually fully amortized over 5 years with mothly paymets. O October 7th, the credit uio will advace Marsha a amout less tha $5,000 such that o November 1st she will owe exactly $5,000. Marsha s first mortgage paymet is due o December 1st. Determie the amout that Marsha is advaced o October 7th. It is ot a leap year. (1) $ 3,816.84 () $ 3,83.03 (3) $ 3,913.34 (4) $ 3,868.18 For additioal help o the topics above, you may wish to review the followig materials: Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios, with a focus o pages 46-64. BUSI 11 textbook Foudatios of Real Estate Fiacig, with a focus o Chapters, 5, ad 7. As well, you may wish to review the HP 10BII CBT tool, specifically the Mortgage Yield Cost Aalysis ad Mortgage Uderwritig ad Borrower Qualificatio sectios. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 7 V. Ivestmet Aalysis The followig sectio will test your kowledge o ivestmet aalysis, icludig et preset value, iteral rate of retur, ad simple icome capitalizatio. THE NEXT TWO () QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A real estate compay is attemptig to market two real estate ivestmets. The forecasted cash flows ad acquisitio costs (at time zero) are show below. Year A B 1 $ 55,000 $130,70 55,000-40,000 3 55,000 110,870 Iitial Costs 10,000 150,000 1. The et preset value (rouded to the earest dollar) at j = 18% o Ivestmet A is: 1 (1) $ 119,585 () $ 8,300 (3) $ -415 (4) $ 45,000. The iteral rate of retur o Ivestmet B is: (1) 4.353584158% () 17.784369439% (3) 15.83806604% (4) 35.5687388658% 3. Aaro has recetly witessed his fried Ali s success with her real estate ivestmets ad he would like to pursue a ivestmet of his ow. At preset, his discout rate is j = 1% per aum. Aaro has discovered a small i that will provide him with the followig cash flows for a ivestmet of $70,000 today: Year Cash Flow 1 $ 0,000 $ 8,50 3 $ 10,000 4 $ 10,750 5 $ 6,500 6 $ 19,000 Cost $ 70,000 The et preset value of Aaro's ivestmet is: (1) $8,10.74 () $8,990.9 (3) $8,59.17 (4) $7,466.90 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 8 4. Calculate the iteral rate of retur o the followig ivestmet, expressed as a effective aual rate. Year 1 $140,000 140,000 3 140,000 Cost (Today) 75,000 (1) 5.575149707% () 4.5775979643% (3) 3.3333333333% (4) Noe of the above 5. Dea Joes would like to purchase Birch Tree Gardes, a icome-producig property located i North Vacouver. He has foud that the market capitalizatio rate is 7.45% per aum, compouded aually, ad that the property has a aual et operatig icome of $148,140. What is the market value of this property? (1) $ 19,884.56 () $1,988,456.38 (3) $1,103,643.00 (4) $,055,473.06 For additioal help o the topics above, you may wish to review the followig materials: Itroductio to the HP10BII Calculator ad Review of Mortgage Fiace Calculatios, with a focus o Appedix B. BUSI 11 textbook Foudatios of Real Estate Fiacig, with a focus o Chapter 9 i the textbook, Foudatios of Real Estate Fiacig. As well, you may wish to review the HP 10BII CBT tool. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 9 VI. Statistics The followig sectio will test your kowledge o statistics basics, icludig measures of cetral tedecy ad dispersio, ad simple regressio. THE NEXT THREE (3) QUESTIONS REFER TO THE FOLLOWING INFORMATION: The followig is a distributio of sellig prices for 1 homes: 110,000 95,000 110,000 450,000 150,000 96,000 140,000 13,000 740,000 150,000 190,000 170,000 6. What is the media sellig price? (1) 140,000 () 150,000 (3) 145,000 (4) 10,333 7. What is stadard deviatio for the distributio of sale prices? (1) $19,09 () $184,06 (3) $33,865,7, (4) $36,944,44,4 8. Calculate the coefficiet of variatio. (1) 88% () 91% (3) 96% (4) 109% THE NEXT TWO () QUESTIONS REFER TO THE FOLLOWING INFORMATION: The followig table provides iformatio o the price ad umber of stories of eight apartmet buildigs: Xi Stories Yi Sale Price 1 $1,000,000 3 $,000,000 4 $4,000,000 6 $4,000,000 8 $5,000,000 9 $7,000,000 11 $8,000,000 14 $9,000,000 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 10 9. The equatio for the best fit regressio lie, usig the least squares method, is: (1) y = 636,400x + 83,700 () y = 636,400x + 545,500 (3) y = 85,500x + 545,500 (4) y = 45,900x + 47,300 30. What is the liear correlatio coefficiet betwee X ad Y? (1) 0.406 () 0.803 (3) 0.977 (4) 0.119 For additioal help o the topics above, you may wish to review the followig materials: BUSI 11 textbook, Itroductory Statistics with Applicatios to Real Estate. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 11 Math Assessmet Formulae Sheet µ ' j m f i (X i ) µ ' µ ' j j m j w i X i w i f i M i F ' j (X i &µ) F ' 1 ( j X i & µ ) F ' j (X i & µ) F ' 1 ( j X i & µ ) Coefficiet of variatio = F µ (100) Y i ' a % bx i â ' j Y i & ˆb j X i ˆb ' j X i Y i & j X ij Y i j X i & ( j X i ) r ' [ j j X i X i Y i & ( j & ( j X i ) ][ j X i )( j Y i Y i ) & ( j Y i ) ] 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia
Real Estate Divisio Math Self-Assessmet Page 1 Math Assessmet Aswers 1. (3). () 3. (3) 4. (1) 5. (4) 6. (4) 7. (4) 8. () 9. () 10. () 11. (4) 1. (3) 13. () 14. (1) 15. (4) 16. (1) 17. (3) 18. (1) 19. (1) 0. (4) 1. (3). () 3. (1) 4. () 5. () 6. (3) 7. () 8. (1) 9. () 30. (3) Detailed aswers ca be foud o the Course Resources webpage. 005. Real Estate Divisio Sauder School of Busiess, Uiversity of British Columbia