HP12cCalculatorSkillsforRealEstateSelfStudyGuide/CertificationTestPreparation

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Copyright2013byRealEstateFinancialModeling,LLC.Allrightsreserved.

HewlettPackard,HPandHP12caretrademarksofHewlettPackardDevelopmentCompanyL.P.

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Overview.TheHewlettPackard HP12c is themostwidelyused financial calculator inrealestate.Youwillseeitinmeetings,boardroomsandonfinancialanalystbullpendesks.Topcommercialrealestatefinanceprofessionalshaveswornbyitsinceitsintroductionin1981(beforeExcelevenexisted!).Unfortunately,whiletheHP12cispowerful,usingitisnot thatstraightforward in that thekeystrokesall seemtobe totallybackwardsvs.whatyourintuitionwouldtellyoutodo.This guide will teach you in plain English the skills and steps critical to successfullyleveragetheHP12cforyourrealestateanalyses.Enjoy!TheREFMTeamQuestionsorcomments?Emailfaq@GetREFM.com

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TableOfContents

OverviewofHP12cCalculatorKeys 41.FinancialRegisters 52.SimpleInterestOnA360Or365DayBasis 63.CompoundInterest 74.PeriodicandAnnualInterestRates 105.NominalInterestRateConversiontoEffectiveInterestRate 116.EffectiveInterestRateConversiontoNominalInterestRate 127.WeightedAverageFunctions 138.DiscountingCashFlows:NetPresentValueandIRR 14 9.ModifiedInternalRateofReturn(MIRR) 1810.AnnualPercentageInterestRateCalculationswithFees 2211.PriceofaMortgageTradedataDiscountorPremium 2412.YieldofaMortgageTradedataDiscountorPremium 26

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OverviewofHP12cCalculatorKeys

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1. FinancialRegisters

What It Is: A register in 12cspeak is a place in the calculators memory where aspecificdatavalueisstoredforuseinanongoingcalculation.FinancialRegistersareasubsetofthemanydifferentStorageRegistersthatthe12cpossesses.Itisimportanttoremembertocleartheseregisterswhenthevaluesarenolongerneeded.Application:Tostoreanumericvalueyouwanttoassociatewithavariable,suchastomake $1,000.00, as a constant Payment Amount, the value associated with the PMTvariable.HowTo:

a. Storeanumberintoafinancialregister:

i. Keythenumberintothedisplay,thenpressthekeyforthecorrespondingvariablee.g.,[n],[i],[PV],[PMT],[FV]

Example:Store90as[n],thenumberofdays

1. 90[n]

b. Recallastoredregistervalue:

i. [RCL]followedbythecorrespondingvariableyouwishtorecall

Example:Recallthenumberofdays1. [n]

c. Clearallthefinancialregistersatonce:

i. [f][REG]

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2. SimpleInterestOnA360or365DayBasis

What It Is: Simple interest is interest that is calculated in each period off of thebeginningofperiodaccountbalance,where theaccountbalancedoesnot includeanyinterestearnedfrompreviousperiods.Theannualinterestratecanbeappliedagainsta360daycalendarora365daycalendar.The12ccalculatesonbothbasesatonce,butdisplaysona360daybasisasadefault.Youcantoggletoseetheamountona365daybasisasdescribedbelow.Application:Tocalculatehowmuchinterestisbeingearnedbyalenderoveraspecifiedtimeperiod.HowTo:

a. Calculatesimpleinteresti. Enterthenumberofdaystobeusedandpress[n]ii. Entertheannualinterestrate,thenpress[i]iii. Entertheprincipalamountborrowed,thenpress[CHS][PV]iv. Press[f][INT]tocalculateanddisplaytheinterestaccruedona360

daybasis.v. Ifyouwishtoseetheinterestvalueona365daybasis,press

[R][x>

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3. CompoundInterest

WhatItIs: Compound interest is interestthat iscalculatedineachperiodoffofthebeginning of period account balance,where the account balance includes the sum ofunreturned principal loaned and unpaid interest amounts that have been earned todate. The key element in calculating compound interest is the specification of thecompoundingperiod,i.e.,theintervalandfrequencyatwhichthecompoundingoccurs.Application: To calculate how much interest is being earned by a lender over aspecifiedtimeperiod,whereinterestcompoundsmonthly,orquarterly,orannually.HowTo:

a. Setupthecompoundingperiodsandinterestrate(usingmonthlyasanexample)

i. Enterthenumberofyearsandpress[g][12x]thisautomatically

entersthetotalnumberofcompoundingperiodsintothe[n]registerii. Calculateandstorethemonthlyinterestrate,entertheannual

interestrateandpress[g][12]thisautomaticallyentersthemonthlyinterestrateintothe[i]register

b. Calculatethenumberofpaymentsorcompoundingperiodsrequiredtopay

offaloan:

i. Press[f][FIN]toclearthefinancialregistersii. Entertheperiodicinterestratewith[i]or[12]iii. Enteratminimum2ofthefollowingmetrics

a. PresentValue,[PV]b. PaymentAmount,[PMT]

a. Ifapaymentvaluehasbeenentered,press[g][BEG]or[g][END]tosetthepaymentmodeasoccurringeitheratthebeginningofeachperiodorattheendofeachperiod

c. FutureValue,[FV]iv. Press[n]tocalculatethenumberofpaymentsorperiods

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Example: Investor X takes a loan of $150,000 at 10% annual interest,compounded monthly, to buy a rental property. If Investor X makespayments at the end of each month of $1,500, how many payments arenecessarytopayofftheloan?Howmanyyearswillittake?

1. [f][FIN]2. 10[g][12]calculatesandstoresthemonthlyinterestrate3. 150,000[PV]4. 1,500[CHS][PMT]5. [g][END]6. [n]

Answer:216Numberofpaymentsrequiredtopaydowntheloan7. 12[]

Answer:18.00Numberofyearsrequiredtopayofftheloan

c. Calculateafinalfractionalpayment(anamountlessthantheconstantperiodicpaymentamount),orafinalballoonpayment(anamountmorethantheconstantperiodicpaymentamount)requiredtopayoffaloan:AFinalFractionalPayment:Letssaythatinsteadof216paymentsbeingneededtopayofftheloan,therewereonly215needed.Thiswouldmeanthatitwouldtake17.91667yearstopayofftheloaninsteadofexactly18.00years.Howdowecalculatethefinalfractionalpaymentamount?

1. 216[n]2. [FV]thisgivesustheoverpaymentamountif216full

paymentsweremade($140.80)3. [RCL][PMT]4. [+]

Answer:$1,359.20

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AFinalBalloonPayment:Letssaythatinsteadof216fullpaymentsbeingneededtopayofftheloan,therewereactually215fullpaymentsneeded,plusapartial216thpaymentthatwasafractionofthefullpaymentamount.Whatisthefinalballoonpaymentamount(payment#215)?

1. 215[n]2. [FV]thisgivesustheremainingbalanceafter215full

paymentsweremade($1,347.96)3. [RCL][PMT]4. [+]

Answer:$2,847.96(thisistheregular$1,500PMTplus$1,347.96)

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4. PeriodicandAnnualInterestRates

What It Is: The rate of interest on a loan expressed either annually or in anotherintervalthatismorefrequentthanannually(e.g.,monthly,quarterly).Application: To back solve for what interest rate is needed, given a frequency ofcompounding,toproduceafuturevalueofagiveninvestmentamount.HowTo:

a. Calculateaperiodicinterestrate:

i. Press[f][FIN]toclearthefinancialregistersii. Enternumberofpaymentsorperiodswith[n]or[g][12x]iii. Enteratminimumtwoofthefollowingmetrics

a. PresentValue,[PV]b. PaymentAmount,[PMT]

a. If[PMT]wasentered,thenenter[g][BEG]or[g][END]tospecifythetimingofthepayments

c. FutureValue,[FV]iv. Press[i]tocalculatetheperiodicinterestratev. Togeneratetheannualinterestrate,enterthenumberofperiodsper

yearandpress[X]

Example:Toaccumulate$10,000in6yearsonaninvestmentof$7,000,whatistheannualinterestraterequiredifitiscompoundingquarterly?

1. [f][FIN]2. 6[ENTER]4[X][n]3. 7,000[CHS][PV]4. 10,000[FV]5. [i] 1.497%isthequarterlyinterestrate6. 4[X]Answer:5.988%

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5. NominalInterestRateConversionToEffectiveInterestRate

WhatItIs:Thenominalinterestrateistheannualinterestrateinnamee.g.,an8%annualrate.However,whenloaninterestiscompoundinginnature,thisnominalrateisin fact lower than the actual, or effective interest rate that results from thecompounding.Application: To find out what rate of annual interest one is truly paying on a loanwheretheinterestcompounds.HowTo:

a. Convertthenominalannualinterestratetotheeffectiveannualinterestrate:

i. [g][END]thissetsthemodeoftheinterestpaymentii. [f][FIN]thisclearstheregistersiii. Entertheannualnominalrateasapercentageandpress[ENTER]iv. Enterthenumberofcompoundingperiodsperyearandpress

[n][][i]v. Enterin100andpress[CHS][ENTER][PV]vi. Press[FV][+]

Example:Calculatetheeffectiveannualinterestrateassumingtheannualnominalrateis6.25%andcompoundedquarterly

1. [g][END]2. [f][FIN]3. 6.25[ENTER]4. 4[n][][i]5. 100[CHS][ENTER]6. [PV]7. [FV][+]Answer:6.398%thisisthevalueoftheeffectiveannualinterestrate

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6. EffectiveInterestRateConversionToNominalInterestRate

WhatItIs:Thenominalinterestrate,istheannualinterestrateinnamee.g.,an8%annualrate.However,whenloaninterestiscompoundinginnature,thisnominalrateisin fact lower than the actual, or effective interest rate that results from thecompounding.Application:Tofindoutwhatrateofnominalannualinterestoneispayingonaloanwheretheinterestcompounds.HowTo:

a. Converttheeffectiveannualinterestratetothenominalannualinterestrate:

i. [f][FIN]thisclearstheregistersii. Enterthenumberofperiodsperyearthenpress[n]iii. Enterthevalue100andpress[ENTER][PV]iv. Entertheeffectiveannualrateasapercentageandthenpress

[+][CHS][FV][i]v. Press[RCL][n][X]

Example:Giventheeffectiveannualrateof5.25%compoundingquarterly,whatisthenominalrate?

1. [f][FIN]2. 4[n]100[ENTER][PV]3. 5.25[+][CHS]4. [FV][i]5. [RCL][n][X]Answer:5.149%thisisthevalueofthenominalannualinterestrate

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7. WeightedAverageFunction

What It Is: Theweighted average is the average of a series of values inwhich eachquantitytobeaveragedisassignedaweight.Application:Tofindouttheaveragepricepaidperlotforlandtobedevelopedintoahousingsubdivision.HowTo:

a. AccumulateStatistics:

i. Dataisenteredusingthesummation[+]key,whichcalculatesandstoresstatisticaldataintothestorageregistersR1R6(theseareknownasthestatisticsregisters).Beforeenteringstatisticaldata,itisimportanttoclearthestatisticregisterswiththefollowingkeystrokes:[f][]

a. Instatisticalcalculationswithonevariable,toenteradatapointreferredtoasthexvaluekeythexvalueintothemaindisplay,thenpress[]

b. Calculatetheweightedaverageofaseriesofvalues:

i. Press[f][]thisclearsthestatisticalregistersii. Keyinthevalueandpress[ENTER]iii. Keyintheweight(numberoftimesthevalueoccurs)andpress[+]iv. Repeatstepsiiandiiiforalladditionalvaluesv. Press[g][xw]theresultantvaluewillbetheweightedaverage

Example:Arealestatebrokerissellingaparceloflandthathasbeensubdividedinto lots. The prices and quantities are as follows: 2 Lots are $200,000 each, 4Lotsare$230,000each,14Lotsare$190,000each,and9Lotsare$290,000each.Whatistheweightedaveragepriceperlot?

1. [f][]2. 200,000[ENTER]2[+]3. 230,000[ENTER]4[+] 4. 190,000[ENTER]14[+]5. 290,000[ENTER]9[+]6. [g][xw]Answer:$227,241

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8. DiscountingCashFlows:NetPresentValue(NPV)andInternalRateofReturn(IRR)

WhatItIs:Theconceptofthetimevalueofmoneyandtheactofdiscountingofcashflowsaretheunderlyingpremisesofrealestatefinance.Theshortversionis:adollartoday isworthmore than a dollar tomorrow, and predictable (safe) cash flows aremorevaluablethanunpredictable(risky)cashflows.TheNetPresentValueisthesumof theTime0 investmentamountand thediscountedvaluesof the futurecash flows,givenanassumedDiscountRate.TheIRRisthatdiscountratethatwillgenerateanNPVof0,orthoughtofanotherway,theaverageannualreturnonthecapitalinvestment.Application:Toperformavaluationofanexistingincomeproducingrealestateassetsuchasanofficebuildingorretailplazabyprojectingandthendiscountingthosefuturecashflows.HowTo:

a. Keyincashflowstreams:

i. [f][REG]thisclearstheregistersii. Entertheinitialinvestment,andpress[CHS]tomakethevalue

negative,thenpress[g][CF0]a. ifthevalueis0,thenenter0[g][CF0]

iii. Enterthevalueofthenextcashflow,andpress[CHS]ifthecashflowisnegative

iv. Press[g][CFj]a. Ifthecashflowamountis0press0[g][CFj]

v. Repeatstepsiiiandivasneededuntildone

b. CalculatetheNetPresentValue(NPV):

i. Oncethecashflowshavebeenstored:a. Entertheinterestrate,using[i]or[12]b. Press[f][NPV]

Exampleonnextpage

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Example:Anincomeproducingpropertyispurchasedfor$100,000incash.Theassetwillbeheldfor5yearsandsoldfor$170,000attheendoftheholdperiod.Theinvestorhasprojectedtheprojectcashflowsasfollows:Year0,100,000;Year1,1,000;Year2,9,000;Year3,11,000;Year4,8,000;Year5,170,000.IftheInvestorsdiscountrateis13%,whatistheNPV?

1. [f][REG]2. 100,000[CHS][g][CF0]3. 1,000[CHS][g][CFj]4. 9,000[g][CFj]5. 11,000[g][CFj]6. 8,000[g][CFj]7. 170,000[g][CFj]8. [RCL][n]9. 13[i]10. [f][NPV]Answer:$10,962.66

c. CalculatetheInternalRateofReturn(IRR):

i. Entercashflowsusingmethoddescribedaboveinsection8(a)ii. Press[f][IRR]

Example:UsingthesamevaluesfromtheExampleabove,calculatetheIRR.

1. [f][REG]2. 100,000[CHS][g][CFj]3. 1,000[CHS][g][CFj]4. 9,000[g][CFj]5. 11,000[g][CFj]6. 8,000[g][CFj]7. 170,000[g][CFj]8. [f][IRR]Answer:15.56%

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d. ChangeCashFlowEntries:

i. Entertheamountintothedisplayii. Press[STO]iii. Enterthenumberoftheregistercontainingthecashflowamountto

bechanged.

e. Tochangethenumberoftimesthatthecashflowamountoccursconsecutively:

i. Storethenumberofthecashflowamountinthenregisterii. Keythenumberoftimesthecashflowamountoccursconsecutively

intothedisplayiii. Press[g][Nj]

Example:Assumingthecashflowisstoredintheregister,changethesecondCFvaluefrom11,000to8,000.ThencalculateanewNPVfora15%return.

1. 8000[STO]22. 15[i]3. [f][NPV]

f. Enteraseriesofinvestmentcashflowsifthenumberofcashflowsexceed20,

andifamongthecashflowsthereareanyequalconsecutivecashflows:

i. [f][REG]thisclearstheregistersii. Entertheinitialinvestment,andpress[CHS]tomakethevalue

negative,thenpress[g][CF0]1. ifthevalueis0,thenenter0[g][CF0]

iii. Givenaninitialinvestmentofmorethanonecashflowoftheamountenteredabove,thenenterthenumberofthosecashflows,thenpress[g][Nj]

1. If[g][Nj]isnotpressed,itisassumedthatthefirstcashflowamount=1.

iv. Entertheamountofthenextcashflow,andpress[CHS]ifthatcashflowisnegative,thenpress[g][CFj].

1. Ifthecashflowamountis0inthenextperiod,press0[g][CFj]

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v. Iftheamountenteredinstep4occursmorethanonceconsecutively,keyinthenumberoftimesthatthatcashflowamountoccursconsecutivelythenpress[g][Nj].

1. If[g][Nj]isnotpressed,thecalculatorassumesthatNjis1fortheCFjjustentered.

vi. Repeatthestepsaboveuntilallofthecashflowshavebeenentered.

Example:Investorlookstopurchasepropertyfor$100,000andhasa15%DiscountRate.Heintendstoholdfor10yearsandsellfor$200,000.YearlyCashflowsareasfollowsduringyears110:$14,000,$11,000,$10,000,$10,000,$10,000,$9,100,$9,000,$9,000,$4,500,$200,000

1. [f][REG]2. 100,000[CHS][g][CF0]Entersthefirstcashflowlineitem3. 14,000[g][CFj]4. 11,000[g][CFj]5. 10,000[g][CFj]6. 3[g][Nj]Entersthenumberofinstancesthattheprevious

linesCFappears7. 9,100[g][CFj]8. 9,000[g][CFj]9. 2[g][Nj]10. 4,500[g][CFj]11. 200,000[g][CFj]12. 15[i]13. [f][NPV]Answer:$1,268.19

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9. ModifiedInternalRateofReturn(MIRR)

WhatItIs:ThetraditionalInternalRateofReturnfallsshortofproducingmeaningfulresults incertainsituations,suchasthoseinwhichtherearemultiplechangesinsign(positivetonegativeamounts)inaseriesofcashflowsinsteadofjustasinglechangeinsign(anegativeinitialinvestmentamount,andeither$0amountsorpositivecashflowsthereafter).ThefundamentalissuewithtraditionalIRRisthatinitscalculation,itisassumedthatall cash flows are either reinvested or discounted at the computed IRR rate. MIRRsolves for this by using userprovided reinvestment and borrowing rates. Theborrowingrateisalsoknownasthesaferate,whichisaratethatreflectsthereturnonaninvestmentinahighlyliquidaccounte.g.,ashorttermU.S.TreasuryBill.Application:Calculate the IRR for an investment that contains a series of cash flowsthatcontainmorethanonechangeofsign.HowTo:

a. CalculatetheMIRR:

i. First,calculatetheFutureValue(FV)ofthepositivecashflowsatthe

reinvestmentrateii. Second,calculatethePresentValue(PV)ofthenegativecashflowsat

thesaferateiii. Withaknownnumberofperiods(n),FVandPV,wecansolveforthe

MIRR(i)Exampleonnextpage

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Example for Annual Cash Flows: An investment group is raisingcapital foravalueaddedrealestateprivateequity fund.Theprojectedcashflows(in$Millions)atthefundlevelareasfollows:Time0:100Year1:7Year2:6Year3:1Year4:0Year5:3Year6:9.5Year7:155What is the MIRR if the assumed safe rate is 3% and the assumedreinvestmentrateis20%?

Step1of2:FindFutureValue(FV)ofthepositive(or$0ifanegativeamount)cashflowsatthereinvestmentrate:

1. [f][REG]2. 0[g][CF0]Investmentcashflowrepresentedas$03. 7[g][CFj]4. 6[g][CFj]5. 0[g][CFj]Negativecashflowrepresentedas$06. 0[g][CFj]7. 3[g][CFj]8. 9.5[g][CFj]9. 155[g][CFj]10. 20[i][f][NPV]$57.6411. [CHS][PV]12. 7[n][FV]7cashflowperiods(Time0doesnotcount

asacashflowperiod)InterimStep1Answer(FVofpositivecashflows):$206.55

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Step2of2:FindNetPresentValue(NPV)ofthenegative(or$0ifa$0amountorapositiveamount)cashflowsatthesaferate:

1. 100[CHS][g][CF0]Investmentcashflow2. 0[g][CFj]Year1cashflow3. 0[g][CFj]Year2cashflow4. 1[CHS][g][CFj]5. 3[i][f][NPV]$100.926. 7[n][i]7cashflowperiods(Time0doesnotcountas

acashflowperiod)Answer(AnnualMIRR):10.77%

Example forMonthly Cash Flows: An investment group is raisingcapital foravalueaddedrealestateprivateequity fund.Theprojectedcashflows(in$Millions)atthefundlevelareasfollows:Time0:100Month1:7Month2:6Month3:1Month4:0Month5:3Months6through11:9.5Month12:155What is the MIRR if the assumed safe rate is 3% and the assumedreinvestmentrateis20%?

Continuedonnextpage

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Step1of2:FindFutureValue(FV)ofthepositive(or$0ifanegativeamount)cashflowsatthereinvestmentrate:

1. [f][REG]2. 0[g][CF0]Investmentcashflowrepresentedas$03. 7[g][CFj]4. 6[g][CFj]5. 0[g][CFj]Negativecashflowrepresentedas$06. 0[g][CFj]7. 3[g][CFj]8. 9.5[g][CFj]9. 155[g][CFj]10. 20[g][12][f][NPV]$162.1211. [CHS][PV]12. 7[n][FV]7cashflowperiods(Time0doesnotcount

asacashflowperiod)InterimStep1Answer(FVofpositivecashflows):$182.00

Step2of2:FindNetPresentValue(NPV)ofthenegative(or$0ifa$0amountorapositiveamount)cashflowsatthesaferate:

1. 100[CHS][g][CF0]Investmentcashflow2. 0[g][CFj]Month1cashflow3. 0[g][CFj]Month2cashflow4. 1[CHS][g][CFj]5. 3[g][12][f][NPV]$100.996. 7[n][i]7cashflowperiods(Time0doesnotcountas

acashflowperiod);thisgivesustheMonthlyMIRRof8.78%

7. 12[X]Answer(AnnualMIRR):105.34%(Note:thisissohighbecausewemadesomuchmoneyinonly7months)

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10.AnnualPercentageRateCalculationswithFees

What It Is: The Annual Percentage Rate is the calculated rate for a mortgage thataccountsforthecashfeesthatborrowersarechargedinconnectionwiththeloan.Application:Calculate exactlywhat a loan is costing a borrower on an annual basisgivenafeeamountpaidupfrontatloanfunding.HowTo:

b. CalculatetheAnnualPercentageRatewithFees:

i. First,calculateandentertheperiodicpaymentamountontheloan:

a. [g][END]b. [f][FIN]thisclearsthefinancialregistersc. Entertotalnumberofpaymentperiods;press[n]d. Enterperiodicinterestrateasapercentage;press[i]e. Entermortgageamount;press[PV]f. Press[PMT]forperiodicpaymentamount

ii. Second,calculateandentertheactualnetamountdisbursed:

a. Ifthefeesarestatedasapercentageofthemortgageamount,recallthemortgageamount([RCL][PV]),thenkeyinthefeerateandpress[%][][PV]

a. Ifthefeesarestatedasaflatcharge,recallthemortgageamount([RCL][PV]);enterthefeeamount;press[][PV]

b. Iffeesarestatedasapercentageofthemortgageamountplusaflatcharge,recallthemortgageamount([RCL][PV]);keyinthefeerate,press[%][];keyinthefeeamount;press[][PV].

iii. Press[i]toreturntheinterestratepercompoundingperiodiv. Toreturntheannualnominalpercentagerate,enterthenumberof

periodsperyearandpress[X].

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Example:Alendercharges2pointstotheborrowerfortheissuanceofhis mortgage. Given a mortgage of $100,000 amortized over 30 yearswithanannual interest rateof6%,what is the trueannualpercentageratethattheborrowerispaying?

1. Enter[g][END]2. [f][FIN]3. 30[g][12x]EntersthenumberofMonths(30Yearsx

12Months)4. 6[g][12]Calculatespercentmonthlyinterestrate5. 100,000[PV]ConvertsLoanAmounttoPresentValue

(PV)6. [PMT]Calculatesmonthlypayment7. [RCL][PV]2[%][][PV]Actualamountreceivedby

borrower(PV)8. [i]9. 12[X]Answer:6.189%

Assumingthesameinformationfromtheexampleabove,whatistheAPRifthemortgagefeeisstatedat2pointsplus$500?

1. [g][END]2. [f][FIN]3. 30[g][12x]4. 6.00[g][12]5. 100,000[PV]6. [PMT]7. [RCL][PV]2[%][]8. 500[][PV]9. [i]10. 12[X]Answer:6.237%

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11.PriceofaMortgageTradedataDiscountorPremium

WhatItIs:Mortgagesareoftentradedinsteadofbeingheldonthebalancesheetoftheissuing bank. They can be sold and bought either at a discount to the remainingprincipalbalance,oratapremium.Application: Calculating a mortgage purchase price given a targeted (desired) yieldamount.HowTo:

a. Calculatethevalueofaloanthatisboughtorsoldatapremium.Given the amount of the mortgage, the periodic payment, the timing andamountoftheballoonpaymentandthedesiredyieldrate,wecanbacksolveforthepriceofthemortgage:

i. [g][END]ii. [f][FIN]thisclearsthefinancialregistersiii. Enterthenumberofperiodsuntiltheballoonpaymentorprepayment

occurs.Press[n].(Followthisevenifthereisnoballoonpaymentorprepayment)

iv. Entertheperiodicinterestrate,press[i]v. Entertheperiodicpaymentamount;press[PMT]vi. Entertheballoonpaymentamountandpress[FV]vii. Press[PV]toobtainthepurchasepriceofthemortgage

Example:Aborrowerelectstoprepayhisloan.Thecurrentannualinterestrateis5%with60monthlypaymentsof$150remainingandaballoonpaymentattheendofthefifthyearof$2,000.Thelenderhaschosentodiscountthefuturepaymentsat5%.Whatistheamounttheborrowermustprepayonthenote?

1. [g][END]2. [f][FIN]3. 60[n]4. 5[g][12]5. 150[PMT]6. 2,000[FV][PV]Answer:$9,507.02

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Example2: A5.5%annualinterestratemortgagewith25yearsremainingandabalanceof$35,000isavailableforpurchase.Whatpricewillgeneratea15%yield?

1. [g][END]2. [f][FIN]3. 25[g][12x]4. 5.5[g][12]5. 35,000[CHS][PV][PMT]6. 15[g][12]7. [PV]Answer:$16,780.57

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12.YieldofaMortgageTradedataDiscountorPremium

WhatItIs:Mortgagesareoftentradedinsteadofbeingheldonthebalancesheetoftheissuing bank. They can be sold and bought either at a discount to the remainingprincipalbalance,oratapremium.Application:Calculating an expected yield amount for a targetedmortgagepurchaseprice.HowTo:

a. Calculatetheyieldofamortgagepurchasedatadesiredprice:

Ifweknowtheoriginalmortgageamount,theinterestrate,periodicpaymentamount,thenumberofperiodicpaymentsperyearandtheamountoftheballoonpayment,wecanbacksolvetowhattheyieldwouldbeforatargetedmortgagepurchasepriceamount.

a. [g][END]b. [f][FIN]c. Enterthetotalnumberofperiodspriortotheballoon

payment.Press[n]d. Entertheperiodicpaymentamountandpress[PMT]e. Enterthepurchasepriceofthemortgageandpress[PV]f. Entertheballoonpaymentamountandpress[FV]g. Hitthe[i]keyfortheperiodicyieldh. Multiplybythenumberofperiodsperyear(e.g.,12[X])

Example:InvestorApurchasesanamortizingloanissuedfor$160,000takenoutat8%for30years.36monthsofpaymentshavebeenmade.Ifthe purchase price of the mortgage is $120,000, what is the annualyield?

1. [g][END]2. [f][FIN]3. 30[g][12x]4. 8[g][12]5. 160,000[CHS][PV]6. [PMT]7. [RCL][n]8. 36[][n]9. 120,000[CHS][PV]

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10. [i]11. 12[X]

Answer:11.15%

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/ColorImageDict > /JPEG2000ColorACSImageDict > /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

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