HP HP10BII Guide

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
USINGTHEHEWLETTPACKARD‐HP10BIIFINANCIALCALCULATOR
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Basicfinancialexampleswithfinancialcalculatorsteps
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PreparedbyColinCSmith2010
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Someimportantthingstoconsider
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1.ThesenotescoverbasicfinancialcalculationsusingtheHP10bIIfinancialcalculator.Thenotesdonotdealwith
theunderlyingtheoryand/orformulae.Studentsshouldideallyhaveaworkingknowledgeoftheundelying
theory.
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2.Atbestthesenotesaredesignedtogetyoustarted.Theydonotclaimtobeacomprehensiveguidetotheuseof
yourcalculator.Consultyourusermanualformoreinformationandfurtherexamples.
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3.Thelogicusedinapproachingtheseexampleswillbesimilartothelogicusedwhenperformingmanual
calculations–theinterestrateisconvertedtoaperiodicinterestrate(i/m)andthenumberofyearswillbe
convertedtocompoundingperiods(nxm).

4.Financialcalculatorshavefunctionalitynotavailabletothehumanbrainandthemulti‐functionalityoffinancial
calculatorsisnotdemonstratedinthesenotes.Ifyouusedifferentfunctionalityandgetthesameanswer–
congratulations‐youareanadvancedfinancialcalculatoruser.Ifyouusedifferentfunctionalityanddonotget
thesameanswerfollowourbasicstepsandreadyourmanualtolearnmore.
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INDEX
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Page
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
GettingStarted
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2
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Lumpsums–PresentValuesandFuturevalues

3
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Lumpsums–InterestRatesandPeriods,andNominalandEffectiveInterestRates
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4
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Annuities–Ordinaryannuitiesandannuitiesdue
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5‐6
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Amortisation–Calculatingtheannualamountofinterestpaidandcapitalrepaid
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7‐9
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Bondvaluation–Calculatingthevalueofannual,semi‐annualcompoundedbondsandcalculating
theyieldtomaturity
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10
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NetPresentValueandInternalRateofReturn
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11
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

GETTINGSTARTED
ColinCSmith20102
Thereareafewthingsyouneedtodobeforewecanstartwiththecalculations.
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FUNCTIONSET‐UP
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TheHP10BIIisalreadysetupasafinancialcalculatorsoitisnotnecessarytosetaparticularmode.
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SETTINGPAYMENTSPERPERIOD
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Inthesenotes,weusethesamelogicusedwith
manualcalculationsandsetourpaymentstoone
paymentperperiod.


HP10BIIfinancialcalculator
KEYSDISPLAY
1P/YR 1.00
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Thisistheorangesecondfunctionkeysituatedjust
belowasimilarpurplekey.
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DECIMALPLACES
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Tosetyourcalculatortotheconventionaltwo
decimalplacesorfourdecimalplaces.


HP10BIIfinancialcalculator
KEYSDISPLAY
DISP20.00
DISP40.0000
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DECIMALINDICATOR
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TheHP10BIIcanshowthedecimalindicatorasa
commaorapoint.


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
./,0,00
./,0.00
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CLEARINGPREVIOUSWORK
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Everytransactioninthisdocumentwillcommence
withthefollowingkeystrokes.CAllisthefunctionto
clearalltheinternalregistersofthecalculator.


HP10BIIfinancialcalculator
KEYSDISPLAY
CALL0.00
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SETTINGFORPAYMENTSATBEGINNINGOFTHEPERIOD
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Ifyouareworkingwithanannuitydueyoumustset
yourcalculatortopeformcaluationsfromthe
beginningoftheperiod.Ifyouaredoinglump‐sum
calculationsorordinaryannuitieschecktoseethat
yourcalculatoriscorrectlysetanddoesnotdispay
“BEGIN”
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
HP10BIIfinancialcalculator
KEYSDISPLAY
IfitdoesdisplayBEGIN0.00
BEG/END 
Removesthis0.00




LUMPSUMS–FUTUREVALUESANDPRESENTVALUES
ColinCSmith20103
*seegettingstarted
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1.SimpleFutureValue(FV)
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YouborrowR5,000fromafriendat8%p.a.interest
tobecompoundedannually.Capitalandinterestis
repayablein5yearstime.Howmuchwillyourepay?


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL 0.00
5,000+/‐PV ‐5,000.00
8I/YR8.00
5N5.00
FV7,346.64
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2.FutureValue(FV)withfrequentcompounding
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YouhavesavedR10,000andinvestthisinafixed
depositwithabankat10.5%compoundedquarterly
for4years.Howwillyoureceivein4yearstime?


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
10,000+/‐PV ‐10,000.00
10.5÷4I/YR2.63
4x4N16.00
FV15,137.38
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3.SimplePresentValue(PV)
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Youhavejustturned20yearsofageandyourlate
UncleScroogebequeathedyouanamountofR5,000
payableonyour25thbirthday.Yourfatheroffersto
giveyouthepresentvaluetodayincash.Atan
interestrateof10%p.a.compoundedannuallyhow
muchmustyourfathergiveyoutoday?Whatisthe
presentvalueofthebequest?

The–veamountreflectswhatshouldbepaidtoday.

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
5,000FV 5,000.00
10I/YR10.00
5N5.00
PV‐3,104.61
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

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4.PresentValue(PV)withfrequentcompounding
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
UncleGeorgeismoregenerousandleavesyoua
substantialinheritance.Youwanttosetasideand
amounttobuyyourdreamcarwhenyoucomplete
yourtraineecontractin5yearstime.Estimatesare
thatthedreamcarwillcostR220,000atthattime.
Abankisofferingyoua5yearfixeddepositat
11.5%compoundedmonthlyfor5years.Howmuch
shouldyouinvesttoday?

The–veamountreflectswhatshouldbepaidtoday.

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
220,000FV 220,000.00
11.5÷12I/YR0.96
5x12N60.00
PV‐124,134.45





LUMPSUMS–INTERESTRATEANDPERIODS,ANDNOMINALANDEFFECTIVEINTERESTRATES
ColinCSmith20104
Thesecalculationsarequitechallenginginanequationformatbutmucheasierwithafinancialcalculator.
*seegettingstarted

5.Calculatingtheinterestrate


AnamountofR400,000isinvestedinasavings
accountthatcompoundsinterestmonthly.After
oneyearthebalanceintheaccountisR464301.81.
Calculatethenominalinterestrate(i.e.thequoted
rateorAPR).

TheR400,000isshownasa–veasthisisthecash
outflowrequirednow.

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
464,301.81 FV 464,301.81
400,000+/‐PV‐400,000.00
1x12N12.00
I/YR1.25
X1215.00



6.Calculatingtheperiods
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
AnamountofR100,000wasinvestedinanaccount
thataccumulatesinterestatarateof14%per
annum,compoundedquarterly.Thebalanceinthe
account,immediatelyafterthelatestquarter’s
interestcreditisR173,398.60.Howlongagowas
theamountinvested?

Rememberthatbecauseyouhavecompounded
morethanonceayear(nxmintheformula)Nis
notyearsbutperiods.Sotheansweris16÷4=4
years.


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
173,398.60 FV 173,398.60
100,000+/‐PV‐100,000.00
14÷4I/YR3.50
N16.00




7.Calculatingtheeffectiverate


Calculatetheeffectiverateof13%perannum
compoundedmonthly.




Thisreflectsthecompoundingperiodsperyear(min
theformula)andcanbechangedtoanyfrequency.



HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN

CLEARALL0.00
13NOM%13.00
12P/YR12.00
EFF%13.80




8.Calculatingthenominalorannualpercentagerate(APR)


Calculatethenominalrate(APR)of14.9342%per
annumcompoundingmonthly.



Thisreflectsthecompoundingperiodsperyear(min
theformula)andcanbechangedtoanyfrequency.



HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CLEARALL0.00
14.9342EFF%14.93
12P/YR12.00
NOM%14.00





ANNUITIES–ORDINARY,DUE,FUTUREVALUE,PRESENTVALUE
ColinCSmith2010
5
*seegettingstarted

9.SimpleFutureValueofanOrdinaryAnnuity(FVA)


AssumeyouputR1,000intoasavingsaccountatthe
endofeveryyearfor10yearsat9.5%interest
compoundedannually.Howmuchwillyouhavein
theaccountafter10years?


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
1P/YR 1.00
1,000+/‐PMT ‐1,000.00
9.5I/YR9.50
10N10.00
0PV0.00
FV15,560.29




10.SimpleFutureValueofanAnnuityDue(FVAdue)


AssumeyouputR1,000intoasavingsaccountatthe
beginningofeveryyearfor10yearsat9.5%interest
compoundedannually.Howmuchwillyouhavein
theaccountafter10years?


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustdisplayBEGIN
CALL0.00
BEG/ENDBEGIN0.00
1P/YR 1.00
1,000+/‐PMT ‐1,000.00
9.5I/YR9.50
10N10.00
0PV0.00
FV17,038.52




11.PresentValueofanAnnuityDue(PVAdue)


Anoverseasbenefactorhasofferedtosponsornew
CareCentreforAidsOrphansinCapeTownandthey
havepledgedtoprovidetheequivalentofR25,000
permonthforthenextfouryearspaymentsstarting
immediately.Thebenefactorwillmakeasingle
investmentlumpsuminvestmentintoabank
accountpaying9.5%interest.Howlargewillthis
initialinvestmentbe?


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustdisplayBEGIN
CALL0.00
BEG/ENDBEGIN0.00
1P/YR 1.00
25,000+/‐PMT ‐25,000.00
9.5÷12I/YR0.79
4x12N48.00
0FV0.00
PV1,002,976.54






ANNUITIES–ORDINARY,DUE,FUTUREVALUE,PRESENTVALUE
ColinCSmith2010
6
12.Calculatingthepayment(PMT)foranormalfinancialtransaction‐AnnuityDue


YoubuyanewcartodayforR120000and
obtainfinancefor80%ofthepurchaseprice
(R96,000)overfouryears.Thebankquotes
youafinancerateof12%perannum
(nominalrate).Instalmentsarepayable
monthlyinadvance.Calculatethemonthly
instalment.


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustdisplayBEGIN
CALL0.00
BEG/ENDBEGIN0.00
1P/YR 1.00
96,000PV96,0000.00
0FV0.00
12÷12I/YR1.00
4x12N48.00
PMT ‐2503.02






Youcanalsosolvefortheinterestrateandforthenumberofperiodsusingthesamefunctions.



13.Calculatingtheinterestrateforanormalfinancialtransaction‐AnnuityDue


AbankoffersyouapersonalloanofR20,000
repayablein24easyinstalmentsofR1,050
permonthstartingimmediately.What
nominalinterestrate(APR)isbeingcharged?

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustdisplayBEGIN
CALL0.00
BEG/ENDBEGIN0.00
1P/YR 1.00
20,000PV20,0000.00
0FV0.00
1,050+/‐PMT‐1050.00
24N24.00
I/YR 2.1237
X12 25.48





Additionalnotes:

PleasealsoseetheBondValuationsectionforsimilartransactions.

Wherewehaveirregularcashflowpayments,wecannotusetheannuityfunctionalityandinsteadcanusetheNET
PRESENTVALUEandINTERNALRATEOFRETURNfunctions.




AMORTISATION
ColinCSmith20107
*seegettingstarted

N.B. ENSURETHATYOUCORRECTLYIDENTIFYYOURPAYMENTSASANORDINARYANNUITYORANANNUITYDUE
ANDSETYOURCALCULATORACCORDINGLY.

14.1Calculatingtheintalment/payment(PMT)foranormalfinancialtransaction‐AnnuityDuewithamortisation



AcompanytakesaloanofR100,000loanrepayable
inequalmonthinstalments,atthebeginningofthe
month,overaperiodoftwoyearsterm,aninterest
rateof12%peryearisquotedbythebank(thisis
thenominalorAnnualPercentageRateAPR.






Thisisyourmonthlyinstalment.

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustdisplayBEGIN
CALL0.00
BEG/ENDBEGIN0.00
1P/YR 1.00
100,000PV100,0000.00
0FV0.00
12÷12I/YR1.00
2x12N24.00
PMT ‐4,660.74




14.2THEAMORTISATIONSCHEDULE–ANNUITYDUE

Wecouldderivetheinterestpaymentsbypreparingamanualamortisationschedule(verytimeconsuming)oronebelow
usingMicrosoftExcel(notallowedinexaminations).

‡Inanannuityduetheentirefirstpaymentisappliedtocapital

Month Instalment Interest Capitalpaidoff CapitalBalance
today 100,000.00
1R4,660.74 ‐ ‡4,660.7495,339.26
2R4,660.74953.393,707.3591,631.91
3R4,660.74916.323,744.4287,887.49
4R4,660.74878.873,781.8784,105.63
5R4,660.74841.063,819.6880,285.94
6R4,660.74802.863,857.8876,428.06
7R4,660.74764.283,896.4672,531.60
8R4,660.74725.323,935.4268,596.18
9R4,660.74685.963,974.7864,621.40
10R4,660.74646.214,014.5360,606.87
11R4,660.74606.074,054.6756,552.20
12R4,660.74565.524,095.2252,456.99
13R4,660.74524.574,136.1748,320.82
14R4,660.74483.214,177.5344,143.28
15R4,660.74441.434,219.3139,923.98
16R4,660.74399.244,261.5035,662.48
17R4,660.74356.624,304.1231,358.36
18R4,660.74313.584,347.1627,011.20
19R4,660.74270.114,390.6322,620.58
20R4,660.74226.214,434.5318,186.04
21R4,660.74181.864,478.8813,707.16
22R4,660.74137.074,523.679,183.49
23R4,660.7491.834,568.914,614.59
24R4,660.7446.154,614.59‐0.00




Year1interest
R8,385.86
Year1capital
R47,543.02
Year2interest
R3,471.88
Year2capital
R52,457.00

AMORTISATION
ColinCSmith20108

14.3 Amortisingthepaymentsusingafinancialcalculatortocalculatetheamountofcapitalandinterestpaidand
thebalanceattheendofeachyear

Thisstepfollowsdirectlyonyourcalculationoftheinstalmentabove.



Weenterthefirstfinancialperiodandthe
numberofpaymentsmadeinthatperiod

Note:Youcansettheamortisationfunctionfor
anyperiodbuthereitisfora12‐monthperiod.

Thisisforperiods1‐12
cCapitalpaidinyear1
dInterestpaidinyear1
eBalanceattheendofyear1

HP10BIIfinancialcalculator
KEYSDISPLAY

1INPUT1212_
AMORT1‐12
=‐47,543.02c
= ‐8,385.86d
=52,456.98e





Forthenext12months(periods13–24)




fCapitalpaidinyear2
gInterestpaidinyear2
hBalanceattheendofyear2

HP10BIIfinancialcalculator

AMORT13‐24

=‐52,457.00f
= ‐3,471.88f
=‐0.02h




YOUCANCHECKTHESENUMBERSAGAINSTTHEAMORTISATIONSCHEDULEinsection14.2thatwascompletedusing
MicrosoftExcel.



15.1Calculatingtheintalment/payment(PMT)forafinancialtransaction–OrdinaryAnnuitywithamortisation





AcompanytakesaloanofR100,000loanrepayable
inequalmonthinstalments,attheendofthe
month,overaperiodoftwoyearsterm,aninterest
rateof12%peryearisquotedbythebank(thisis
thenominalorAnnualPercentageRateAPR.





Thisisyourmonthlyinstalment.

HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CALL0.00
1P/YR 1.00
100,000PV100,0000.00
0FV0.00
12÷12I/YR1.00
2x12N24.00
PMT ‐4,707.35





AMORTISATION
ColinCSmith20109
15.2.THEAMORTISATIONSCHEDULE–ORDINARYANNUITY

Asforthescheduleat14.2thiswaspreparedusingMicrosoftExcel.

Month Instalment InterestCapitalpaidoff CapitalBalance
today 100,000.00
1R4,707.351,000.003,707.3596,292.65
2R4,707.35962.933,744.4292,548.23
3R4,707.35925.483,781.8688,766.37
4R4,707.35887.663,819.6884,946.68
5R4,707.35849.473,857.8881,088.80
6R4,707.35810.893,896.4677,192.34
7R4,707.35771.923,935.4273,256.92
8R4,707.35732.573,974.7869,282.14
9R4,707.35692.824,014.5365,267.62
10R4,707.35652.684,054.6761,212.95
11R4,707.35612.134,095.2257,117.73
12R4,707.35571.184,136.1752,981.56
13R4,707.35529.824,177.5348,804.03
14R4,707.35488.044,219.3144,584.72
15R4,707.35445.854,261.5040,323.22
16R4,707.35403.234,304.1236,019.10
17R4,707.35360.194,347.1631,671.95
18R4,707.35316.724,390.6327,281.32
19R4,707.35272.814,434.5322,846.79
20R4,707.35228.474,478.8818,367.91
21R4,707.35183.684,523.6713,844.24
22R4,707.35138.444,568.909,275.33
23R4,707.3592.754,614.594,660.74
24R4,707.3546.614,660.740.00


15.3 Amortisingthepaymentstocalculatetheamountofcapitalandinterestpaidandthebalanceattheendof
eachyear

Thisstepfollowsdirectlyonyourcalculationoftheinstalmentabove.


Weenterthefirstfinancialperiodandthe
numberofpaymentsmadeinthatperiod.The
amortisationfunctioncanbeforanyperiodbut
hereitisfora12‐monthperiod.

Thisisforperiods1‐12
cCapitalpaidinyear1
dInterestpaidinyear1
eBalanceattheendofyear1

HP10BIIfinancialcalculator
KEYSDISPLAY

1INPUT1212_
AMORT1‐12
=‐47,018.47c
= ‐9,469.73d
=52,981.53e




Forthenext12months(periods13–24)






fCapitalpaidinyear2
gInterestpaidinyear2
hBalanceattheendofyear2

HP10BIIfinancialcalculator
KEYSDISPLAY

AMORT13‐24

=‐52,981.59f
= ‐3,506.61f
=‐0.06h




YOUCANCHECKTHESENUMBERSAGAINSTTHEAMORTISATIONSCHEDULEABOVE.
Year1interest
R9,469.73
Year1capital
R47,018.47
Year2interest
R3,506.61
Year1capital
R52,981.59

BONDVALUATION
ColinCSmith201010
*seegettingstarted
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16.Valueofanannualpaymentbondwithasingleannualpayment


Acompanypurchasesbondson1Januaryofthis
year.Thenominal/face/couponvalueisR1,000and
theannualnominal/couponinterestrateis10%.The
bondisredeemableon31December6yearslater.
Themarketinterestrateforsimilarbondsis15%.
Assumethatthebondpaymentsaremadeannually
inarrears.Whatpricewouldthecompanypayfor
thebond?(i.e.whatshouldthevaluebeon1
Januaryofthisyear?




HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CLEARALL0.00
15I/YR15.00
6N 6.00
1,000FV1,000.00
100PMT 100.00
1P/YR 1.00
PV‐810.78
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17.Valueofatypicalgovernmentbondwithsemi‐annualpayments


Assumesameinformationasfor16aboveexcept
thatthebondisatypicalgovernmentbondthat
payssemi‐annuallyinarrears.Whatpricewouldthe
companypayforthebond?




HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CLEARALL0.00
15÷2I/YR7.50
6x2N 12.00
1,000FV1,000.00
100
÷
2PMT50.00
1P/YR 1.00
PV‐806.62




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18.Calculatingtheyieldtomaturity

Thisisextremelydifficulttocalculatewhenusingaformulaapproachwithoutafinancialcalculator.


Thenominal/face/couponvalueisR1,000andthe
annualnominal/couponinterestrateis10%paid
semiannuallyinarrears.Youpurchasedthebondon
1Januaryofthisyearandthebondisredeemableon
31December10yearslateratapremiumof10%.
ThebondispricedatR980on1Januaryofthisyear.
Whatistheyieldtomaturityon1Januaryofthis
year?

‡ Rememberthatthisistheratefor6months.
Toannualisetheconvention(frombond
tradingintheUnitedStates)hasbeento
multiplythisby2.


HP10BIIfinancialcalculator
KEYSDISPLAY
*MustnotdisplayBEGIN
CLEARALL0.00
10x2N 20.00
1,000x1.10FV1,100.00
980+/‐PV‐980.00
50PMT 50.00
1P/YR 1.00
I/YR5.45
X2 10.91
‡
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