THEORY OF INTEREST STUDY NOTES
Notation
a capital C
Accumulation_S or A
Interestrate eg i 12,75i pa or i 0,1275p u p a
COMPOUNDINTEREST i'm nominal interestrate
m
i y effectiveinterestrate
FINDNUMBEROF INPERIOD
ecs
1
o
in o papa iii no I fear
mY
i matters
numberofquarters
17,5144 4 14quarters
year79th year
moaning
so
es
i µo
19 17,31 12 27months
0N FINANCIAL CALCULATOR
60
eg Fv 6825,15 71 01,1245
on calc
6825,15 I EvQPMI14,5 III I F 60 1 he
1314031,002
,tow capital a principal amount grows
let k 100 1 10 1
simple interest
5 100 it 0,7N 100 t Ion
n I 100 t 10 1 S k it in
sa
22
10
n 2 100 t 10 linearincrease
n 3 100 t tox 3 It s
time
compound interest
5 100 7 to 1 n n
100 X l l
n
sa
s k Iti
n r too x 1,1
exponentialincrease
n z too 1,12
n 3 100 x 1,13
EXAMPLE
FindFroerusoinvestedat asimpleinterestrateof171 p a for3years
5 225611 30,111 133000,48
HowmanyyearswillittakeRsoootoaccumulatetorsiboat a simpleinterestrate of9 pa
5160 3000Citnco09
i n syears
EXAMPLE CALC
FindaccumulatedamountofR5000investedatrate of 121 p a compounded sooo Pro
halfyearly for 7years izI 2r
5 50001110,0614 1211304,52 14 N
o pmt
to rv
FindtheProeadestofrsooopayable in byearstime if interestis calculated
at aneffectiveinterestrate of m l p a for the first 2 years then 141 pa care
compoundedtwiceperyear I sooo opmi
sooovb.o.ro OK 14
8000C o
2min06 6
pv rv
n ip
R4747,61 a
pv
,moreexamples
whatinterestrarep acompounded a annually ebmonthly willRasooaccumulateto
nooooin 9years
asoocitis noooo 7sooCiti 08 16ooo
wit 2.133 o.ooi
oyp.u.rsmonon
Citi 2,133m
ii o.osassp.iepa i ich 8,448 p a
ors.issy.rsa
0Howlongwill R5500 at a bank at i21 0,09pu p a taketo accumulate to1310000
calc
10000 550040.045 n sooo proopmro
oooo
c0455 1.81
a 2p
nenco.us enci.si
enci.sm
is.ssnaieyrsenci.o
45 Gitayears
gi.n
solvefor
Rx wasinvested at i 0,16P U p a 5 yearslater R7000
wasadded after 8 years theaccumulated amount
was 1319500
x 19500 too soo
I
o 1s I
8
CALC
option OPTION 2 I iasoorvoopm
20 70001110,04112 19500
ocxuto.ae
X 195004 7000
2363.94
7c no
n
4p
11 19500 4.7000 9 tooo
so
PD
, Nominal effective rates
ccm nominalp a
NOMINALRATE quoted i effectivep a
im
aiw.ausmgi.cz aeffectivepertmenyear
EFFECTIVERATE period
earnover
actually
m
m
annua
genuine
s Kati n
s Kationmymxn
heneceiverateperemenyear
eg iai pa compoundedguan
eny
in in
s Kat eeeeceive
quarterly
Kato an rate
CORRESPONDING1EQUIVALENT INTERESTRATES
whendifferentinterestratesgivethesameresult
eg.rzoogrows i
ai.p.aforsyrszoocito.oas5
so7iaus
equivalentrate with c ompounding
monthly
25
zoou i 307,7248
i s.oxsia i
o.osoasaap.u.p.ci
it In i imf
nm
amescenario i find equivalentannualrate compoundedmonthly
page19intextbook
it 0,0915 it i 60 CALC
ONCALC i ti pv o PMT
solve i 8,64879 is inn 2 PIYA
2 N
rv r
ore
is nom 2 PNREFF
Notation
a capital C
Accumulation_S or A
Interestrate eg i 12,75i pa or i 0,1275p u p a
COMPOUNDINTEREST i'm nominal interestrate
m
i y effectiveinterestrate
FINDNUMBEROF INPERIOD
ecs
1
o
in o papa iii no I fear
mY
i matters
numberofquarters
17,5144 4 14quarters
year79th year
moaning
so
es
i µo
19 17,31 12 27months
0N FINANCIAL CALCULATOR
60
eg Fv 6825,15 71 01,1245
on calc
6825,15 I EvQPMI14,5 III I F 60 1 he
1314031,002
,tow capital a principal amount grows
let k 100 1 10 1
simple interest
5 100 it 0,7N 100 t Ion
n I 100 t 10 1 S k it in
sa
22
10
n 2 100 t 10 linearincrease
n 3 100 t tox 3 It s
time
compound interest
5 100 7 to 1 n n
100 X l l
n
sa
s k Iti
n r too x 1,1
exponentialincrease
n z too 1,12
n 3 100 x 1,13
EXAMPLE
FindFroerusoinvestedat asimpleinterestrateof171 p a for3years
5 225611 30,111 133000,48
HowmanyyearswillittakeRsoootoaccumulatetorsiboat a simpleinterestrate of9 pa
5160 3000Citnco09
i n syears
EXAMPLE CALC
FindaccumulatedamountofR5000investedatrate of 121 p a compounded sooo Pro
halfyearly for 7years izI 2r
5 50001110,0614 1211304,52 14 N
o pmt
to rv
FindtheProeadestofrsooopayable in byearstime if interestis calculated
at aneffectiveinterestrate of m l p a for the first 2 years then 141 pa care
compoundedtwiceperyear I sooo opmi
sooovb.o.ro OK 14
8000C o
2min06 6
pv rv
n ip
R4747,61 a
pv
,moreexamples
whatinterestrarep acompounded a annually ebmonthly willRasooaccumulateto
nooooin 9years
asoocitis noooo 7sooCiti 08 16ooo
wit 2.133 o.ooi
oyp.u.rsmonon
Citi 2,133m
ii o.osassp.iepa i ich 8,448 p a
ors.issy.rsa
0Howlongwill R5500 at a bank at i21 0,09pu p a taketo accumulate to1310000
calc
10000 550040.045 n sooo proopmro
oooo
c0455 1.81
a 2p
nenco.us enci.si
enci.sm
is.ssnaieyrsenci.o
45 Gitayears
gi.n
solvefor
Rx wasinvested at i 0,16P U p a 5 yearslater R7000
wasadded after 8 years theaccumulated amount
was 1319500
x 19500 too soo
I
o 1s I
8
CALC
option OPTION 2 I iasoorvoopm
20 70001110,04112 19500
ocxuto.ae
X 195004 7000
2363.94
7c no
n
4p
11 19500 4.7000 9 tooo
so
PD
, Nominal effective rates
ccm nominalp a
NOMINALRATE quoted i effectivep a
im
aiw.ausmgi.cz aeffectivepertmenyear
EFFECTIVERATE period
earnover
actually
m
m
annua
genuine
s Kati n
s Kationmymxn
heneceiverateperemenyear
eg iai pa compoundedguan
eny
in in
s Kat eeeeceive
quarterly
Kato an rate
CORRESPONDING1EQUIVALENT INTERESTRATES
whendifferentinterestratesgivethesameresult
eg.rzoogrows i
ai.p.aforsyrszoocito.oas5
so7iaus
equivalentrate with c ompounding
monthly
25
zoou i 307,7248
i s.oxsia i
o.osoasaap.u.p.ci
it In i imf
nm
amescenario i find equivalentannualrate compoundedmonthly
page19intextbook
it 0,0915 it i 60 CALC
ONCALC i ti pv o PMT
solve i 8,64879 is inn 2 PIYA
2 N
rv r
ore
is nom 2 PNREFF
