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Math 166 - Week in Revi€w #!0
ChapterF - Finance
. Simple Int€rrst - interest that is computedon the original principal only
. Simple Interest Fornulas
Interest=1:Prl
AccumulatedAmount= A
P I : P + Prt : P( | + rt)
- +
NOIIATION: 1 = interest earned,P = principal, r = interest rate (as adecimal),
, = term of the investm€ntin fEAfiS, A = accumulat€damount
. The TVM-Solver CANNOT be used for simple interest calculations.
. Compound Inter€st - eamedinterest thal is periodically addedto the principal and ihereafter itself earnsinteresr
!t the samerate.
. The TVM-Solvercanbe usedin problemsinvolvingcompoundinreresras follows:
= total numberofpaymentsmade,usuallyr, x t.
N
= interesrrateinlerc?ntlorm. Don't convertto decimalformll
IVo
= presentvalue(prinicpaltor the amountyou startwith). Enteredas negativeifinvested,
PV
positiveifborrowed.
PMT = payment(amountpaid eachperiod).Enteredasnegativeifpaying otTa loaD,positive
if receivingmoney,0ifcomputing compoundintercst.
=
FV
futurevalue(accumulated
amount).This will be 0 ifpaying off a loan.
= numberof paymentsperyear(usuallythe samea9m).
PN
= numberofconversionsper year(lrl).
C/Y
. At thebottomofthe screen,youwill se€PMT:ENIDBEGIN.IfEND is highlighted,thentheTVM Solvercalculates
everythingwith paymenhbeingmadeat the endof rheperiod. For virtually all ofthe problemswe will work in
class,END shouldbe highlighted.
. You cansolvefbr anyquantilyon lhe TVM-Solverby movingthecursorto thatquantityandthenpressingALPHA
fbllowedby ENTER.
. Effective Rate of Int€rest - The effective rate of interest is a way of comparing interest rates. More precisely, tbe
efectiw rate is the simpleinterestratethatwould producethe sameaccumulated
amountin I yearasthe nominal
p€r
y€ar.
m
times
rate compounded
. The effectiverateofinterestis typicallydenotedby r.// andis alsoknownas rheeffectiveannualyield.
. To calculatethe ettbctiverareofinterest,usethe EftI ) tunctionon the calculatorThis tunctioncanbe found under
Finance-juslarrowdownuntil you seeC: Eff(.
. The Eff( ) function has two parameters,t}e nominal (or annual) interest rale enteredas a percenr,and the number
of conversion,rr, per year: Efi(nominal rate as a perc€nt, ,1)
. Annuity - a sequence
ofpaymentsmadeat regulartime intervals.
. ln this course,we will studyannuitieswith the following properties:
1. The termsaregivenby fixedtjme intervals.
2. The periodic paymenis are equal in size.
3. Thepaymenlsaremadeat the endof the paymentperiods,
4. The paymenl periods coincide with the inlerest conversionperiods.
Page2
h16Flrrmotsdahmy
l. Jakedeposited $350 into an accountpaying 3.25% simple interest. How much money is in the accormtat the end
of4 years?How much inrerestwaseamed?
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2. WhenEricagraduatedfrom high school,shercceived$500frcm her parcntsasa gift. Shethanloancdthis money
to herbrotherwho iepaidher 3 monthslaterwith a sumof $510.25.Whatwaslhe simpleinterestratethat Erica
chargedherbrother?
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!t)' ]5 : 5uO* c Ta
= a'?ttu
ro
.
a
s
c:
/(*o*z/P-\
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Shewill need$4,500for this trip,
3. Anncttewantsto takea trip to Buropewhenshegraduates.
(a) How muchmoneyshouldAnnettedepositnow into anaccountpaying8%/yearcompounded
quarterlyif she
-frfriolvt'
graduate
yea6?
in
4
a\pectsto
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}potr+-ite18,ot
lB-Ll1--4
\rill sheeamin the4 years?
Howmuchinterest
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la.rntd= IAOO-bA 1g.0l
$ raat.qq
(c) How muchinlerestwill sheeamin thethjrd quarterof the s€condyear?
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Page3
Md16FirmoHt*ilNt
4. Lynn, Annette's twin sistel wants to take that sametrip to Europe,but shedoesnot haveenoughmoney to open th€
sirmetype of account as Annette. Instead, she plans to make monthly paymentsto an account paying 8.25%/year
cornDoundedmonthlv.
(a) How muchshouldeachpaymentbe so rhatshehas$4.500al rheendof4
N'l*x4
f,\o=$'2-<
[V'0
fu. 46Dr
f l\'All'11-,
O) How muchintercstwill Lynneam?
LSnn's
{o*aa.J4o6i.t= 14 +5 x l7-/-+-- l V 8 l b . uo
, = ,4OO_ltlz,tto = 1 b yb .4o
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{,wxf tS+tA(AlA
5. Kim openedan accountp ying 5.25%ly.ar cornpounded
monthlywith $100andplansto add$50 at the endof
eachmonthuntil shehasat lea$ $45,000.
(a) How longwill it lakeherto first r€achhergoal?
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{ 9o 5.45
/r,q( -5D
( '/ '' 451)00
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to 1l.ob lt[L,'1tw,r15
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(b) How muchwill sheactuallyhavein theaccountwhenshefirst reachesher goal?
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(c) How muchintrres!will Kira ealnin the third monthof her sixthvearof makinsthis investrnent?
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6. Benjamin is 25 yea$ old and plansto retire in,{O years. Whenhe retil€s, he would like !o receivemonthly payments
of $3,000 from a rctircment accountfor 15 years.
(a) How much money should Bedjamin deposit at the end of eachmonth from now until he rctircs to achievethis
goal if he s€curcsan accountthat will pay 6.25%/year compoundedrnonlhly for the life of the account?
"
rcmnt
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n@
(c) How muchintcrestvrill bc earncdovertheentirelife of thaaccount?
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- a| ?.^4Juliafi
op€nedanaccountwith $8,000andaft€i 7 yoars,it hadgrownto $10,000.
-
(a) Whatwastheannualinter€strateif interestwascompounded
weekly?
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O) If the annualidtercstrate foundin pan (a) wasinsteada simpleinterestratc, how long would it takc
Julian's$8,000to growto $10,000?
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Page5
Md 1 6 F d r m o H l e b r t
8. Mles and Keiko are shoppingfor a new home. They can afford a down paymentof $25,000and monthly payments
of at most $850. Bank A has offered to financr-a loan at 8.75%/yearcompoundedmonthly for 30 yean, whereas
Bank B has offered 8.25%/yearcompoundedmonthly for 25 yean.
(a) Wllat is the most exp€nsivehousethey can afford to buy? Which bank would they have to usefor this house?
inter€stdid theypay?
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lv asooo ft-4ly=t,
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ltat a*tt pil n I oan i/10'ttX
h U r r s lf t d d - -9 o t)o {+-t\o o o = $ llb,ur+
xar=faarr,9
Tov.ro*t pl athrwe -- $15ooo
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{t)e.(t$+
ae=lItt05tl - lto oar
(c) Referingto part O), createanamortizationschedulefo. thefi$t 4 monthsof the loan.
mletesl
period
0
)-4
2
3
4
payment
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;c6 . lq lo'1o.lg.
ia2,41 010,t(
amounttoward
principal
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kla , ?1
1b - 1 q
(1 . d
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%nDDf oxrs/tu
outstanding
principal
aso0{)
44qt+,1D
q4$ 21 .Sl
84 1LlD.aa
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Page6
Miirfitura@l]dri.@
9. If Bank A has a savingsaccount paying E%/y€arcompoundedsemiannually and Bank B offels 7.9q'/yeat compoundedmonthly, which is the better offer?
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10. Juanitadecidedto purchasea flat-scre€nHDTV. Shemakesa downpaymentof $250and securcsfinancingfor
the balanceof the purchaseprice at a ratc of l2%/year compounded
mondlly. Underthe tarmsof the finance
agiccment,shcis requiredto makemonthlypaymentsof $125for 30 months.
(a) Wlat wasthecashpricc of th€TV?
Fi^it [0i., a-tr^t:
N'3t:
Le'n t''4t
[tdr,, pr;rl.= ?orn Prlt++
Prnf.'le-s
= dSD+V7?Y'1b
('t'- o
\').
?11-clv=
7I:::e
lfr-n*t=$ 5aa1.sv
O) How muchinterestdid Juanitapay?
.
tt +al o,rt+ym;/ o^ l&4
125 x 6t) = iV1tu
=
-b179'1b 2'
fuMail pa|d. Vlso
/ o , n wl a ^ n P A '- a sD + Ias ' 43o ; 4D' o
(
,\
r*.rr,t ?L= 4ooo-3411 9t=l4 5r4'D{ I )
11. Deannaowes$l,0OOon a crealitcardthathasan inre;;fT;i6iFi3%/year
minimumpaym.ntof $20cachmonth,
(a) how muchofher first paymentgo€stowsrdintcrcst?
f,4.lBtttlv'rct-- tolo* o,glt/tl"
compounded
monthly.If shepaysthe
f rc.14
O) howlong wiU it takeher !o pay ofi thecard?(Assumeno additionalchargesarcmade.)
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ru,lEAri(2(ttz>
1114fi
purchased
12. TheGardners
a vacarion
home15yearsago. At rhetimeoLhgllurchase,
thei wereabletb makea
p4?6Eiioi:CDf
purchase
price
the
and
$en
securea
a
toan
o($-l
oY.od}f
finance
rheremainingamounr.
{d6in
wift mo;lhlypaymenrs
\fi-.16#6iiii6ironized
o!er 30yearsaran r'\ita/stmreof 6.75%/year
compounded
rnonthly.
. (a) Wlat is rhecurent ouhtandingprincipalon the loan?
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5luoliF,^l
'r
N- -l a * a o
1(p7'. F tatl 6ulskadi^9
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= lhl]N 6Jl
M
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? v' 1
P{"lliooo l l t - c l y . 1 v
fu r*f1lr-IA
t)
I o r b a ( ( ta .*tr ) :
(b) How mucheqlity do theGardnershavein iheir vacationhome?
Itrit
tt^":(d'
- w$l^t{4xst;ll0t4x
- 1 b a 5 q '5 1
= ftl,e$
15q!| c D . 4 3
(c) Overthe 3o-yearperiod,how muchinterestwill the Gardnerspay?
$ltkl on v llx 30-: +24" l'lt2so
il*+ ya att loa*
^'t/' ''70.8u=
fuu(rtsr
F'd i:::,-*='
losao
= B t4o.tlo,rol
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I 3. Find theeffectiverateof 6% per yearcompounded
semiannually.
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