ip t aRate Retain
future Make grouthrett
start with amount N today If this amount gives of
rte R how much will we have after n periods raft
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n g ni 1000 1 003
fieri E Et le EMI
and smh to double your wealth
How long will it take a
35 Year 14 year
Multiple compoding
Suppose intent is paid m
will we have after 1 years stating from ser
Quoted interest rate R APR Howmuch
Fri reel D Years I
Va1000 R lol peryear annual compounding
FY 1000 ly of
If m 4 quarterly coupondig
1000 it1010
M z semi annual compounding
o.glD I 1000 it ypfD
1000 ie monthly compounding
Continue this line
A ninth In the limit
woo.tn i compoundinch
Continuous
Ireened of 2 t for the 1styear Suppose our wealth grows
4 31 for the 2nd year what is theoverall
Period Return
at time to at price Pe
the asset of time of price Pe
gouth rate Assuming
start with v annual compounding
FV 100011 022
After 2ndyear
Assuming continuous compounding
fuzz 1000 1styear FV woo I 02 3
After 2nd year FL 1000 é 1000
Theall goth
is the price at the end of month
t Peis theprice attheendofmonthtt
Rt tiff Y DPE
she met return
gross retain Mst
971 Cet Rt
IE i YI IIE
nineteen one 2 months
It Rely are
I t Ry t Rft t Rt Re l
Rei t Re Rei gifRt ifaool
Rea ootouzt1
Rt2 I0.01002 01
dividend this month
Pt 990 Suppose MSFT also paid a
Rt Rta RE2
Annual Felter A
annual MSFT return mm
every month
the 2 month setter on MSFT is 12 51 the annual reterm
1 0.125 1 1 0273 m
Suppose the monthly returns once n tone periods are
Arithmetic Average
Suppose the simple net return a Rt for ninth t
The continuous compounded return formonth
Ritt a 50 01 i oso 10.50
rely log lit Reta log Eg log ly Pt
oases Approximation of Rt is smell then I GARE E
M MtfhGnhmi
Pt z freesareerff
rey 8 12 r
Annuelizing
If each return is IVei VE2
t the same
th z a Veere ereze
re r t refer
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