This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: wm———————————_——_———n——————————————""""HIIlllllllllllIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'IIIIIIIIIIIIIIIIIgI Learjjﬁﬂ Lecture 7 e45
Lumgsum Future Value and present Value In this example, what are the values for the following variables?:
F U I P I c
Deﬁnitions: PV = {00 ‘00 1H I) fillOZ'S
*r’pv: ﬁle'seﬁrvaru‘ér relate1, r =  OS
Ika—y Future Value aw VF M = l
l or r a anm'linte—rest) rate (annual percentage rate or APR) N = ' X133—
M —+ number of compounding periods per year; the frequency of compounding
r") " I 7      —m~ Mamet 1"  (3' f  bl I f d th ﬁfth
Rigor rlM r» intrapenod, or periodic interest rate a I‘ ﬁatIrma“? * I I ﬂy W
N a total number ofﬁeriods] (M x number of years) % qu“ a “5 ’3'} ‘ I Example 1: You put $100 into the bank today at 8% annual interest. What is it worth in H I J" 6 years? TlMELINE: If._._t_ﬂr4—a: *9
‘Jx‘J‘t'f‘rT N034 ‘ 3N I
. _—, IOO we
; Future Value PV
! I I r = .
l I If we put $100 In the bank today and earn Interest of 5% per year (annual compounding). 08
' what do we have after two years? I M = i
TIMELINE: N = M l ‘lo
lac _.—+ “30L! 5'5) ——— 2' {OS tn? tuna: I la , ﬂ
FV= va [1 + rlM1N= :ook Hedi} : I. see First year: $100 x (1 + .05) = $1 x 1.05 = $105, or our original $100 Plus $5 interest. Second year: $105 x (1 + .05): $105 x 1.05 = 311025 What if we havewcompounding? :I? II
or, TIMELINE: I Mfg ;
.0 ‘
$100 x (1 + .05) x (1 + .05) = $100 x (1.05)2 = 511025
PV = :00
Fv~=2..=5%{$100}= $100 x(1os)2= $110.25, r= m
or’ M T. : N = U \{9 :ﬁq_
FV PV x [1 + rlM] This IS the Future Value Formula (FVF) N ' IN _ _ I 0 CE, I 2& III
FV= PVX[1+rlM = goo a :7 W where r is the interest rate per year and N is the total .
between the PV and W (in this caso Years). number Of Compound'”9 peliOdS in this example, each compounding period is 3 months, and there are 24 of them over
the 6 year period. 6  Richard T. Bliss, Babson University
I I and Terry D. Nixon, Miami Univexsity
9  Richard T. Bliss. Babson Univasru I
and Terry D. Nixon, Mimi University PM 301 AB — Fall 201‘! 44 l 45 FIN 301 AIB _ Fan 2011 ﬁg Ear«me v ' a i Lecture? 1:? A ‘m‘aﬂ e47
Example 2: You have $300 to invest for four years. Key Bank is offering 5% 3 Example 3: What is the value today of $3,000 received in two years? The interest rate
comeUnded annuaﬂyi while the Fifth—Third’s rate is 4.9% APR. bUt With daily i '3 6% compounded annually 0 ‘ "—77 W 7 iii
compounding. Where do you put your money? TIMELINE: I .mﬁ‘, A,“ 3ND I ‘93 I
KeyBank PV= a.” r: L; M=‘= rIM=f N= $4; FV: 3mg
. L" r =  0b
TIMELtNE: “H """mo'm‘F‘ M = i
N = In i =7.
Fv=var1+r/M}“= gipgatzgcyt W
~ I II .1 : ' 3 Q ,4 n
PV= FV +{1 + rIM]N = 0:, I : Zack13*;
{\1 + . .  ~ .0433
———_F'ﬁh‘Th"d PV = r = . M = 10g? TIM = N = 7m? Example 4: How much must you invest in the bank today if you want to have $1,500 ‘
o L «it after 4 years? Interest is 11% compounded annually; TIMELINE: Engmoi; ' TIMELINE: c—Wc—fﬁ ‘ 3W 7 ism
Fv=vat1+rrM]”= gmw Wot 19W? I" FV= E7300
3 “'3 3 131“? J? N= 4177\i2’wr PV=FV +[1+rIM]N= .— What if the bank pays 11% APR compounded monthly? 8 l U L's’f
e urvaient vaiue of cash . we are °°king for the L—ui—s —r4~—*"
T: ff d' thﬂoi: at a date mono the" recetpt) TIMELIN E1 ? fix
e process 0 in mg 9 of future ca . _ _ t
the PU formula from above: Sh ﬂows '5 called d’scoum‘w We begin With _
FV = 5"“
= N = i
FV PV x [1 + rfM] now rearrange this to solve for PV [VI _ is
W = + ~ . . N = am at
FV [1 + rlM] This IS the Present Value Formula (pVF)
f («r r ,2; PV=FV +[1+r/M}“= ism 1T «57 a ’ ~
‘7—
©  Richard T. Btiss, Babson University
and Terry D. Nixon, Miami University
©  Richard T. Bliss, Babson Unitas“)t FW 301 A 8 F31! 2011 “new 0. Nixon. Miamiummiw l 45  ' 47 FIN 301 AB — Fair 2011
:.‘.‘ _ _ a e48
Lecture? ﬂ , /’ /, Note that more frgguent comgounding means ailsmaller investment Edgy. In other words our money grows faster. Why? 7 El Practice: How much would you have to invest today if the bank paid 11% compounded daily? 955;}; §glving Emblems Where N or r an: unknown. Example 5: You have $6,000 today, but need $9,000 for the down payment on a new
sailboat. If you put the money in a bank that pays 12.5% compounded annually, how long before you are able to make the purchase? N TIMELINE: F"‘“"J');—_'wu—‘_—_H“‘*—~am]
but 90%;?
PV = to?
FV = ﬁ‘
r = '.
M :
r/M = ' «r l
N : can plug in the variables and solve for 
“Mfg”; MW OK
I ‘ . :3. no 5
P W ili+h5m52,
i ’1 i ‘lh '» I ‘ ..
vow: rials—J; Woman
l _ i1 l
U iriiij‘i iii—i
1 Fix “ _ i. 'P(' F14 { x
FIN 301A,B ~Fali2011 f .l" i.‘ h“ e  Richard r Bliss, Babson University
and Terry D. Nixon, Miami Univewu MW; EMMA fairway;le What if the interest is 12.5% APR compounded monthlﬂ Will the time be shorter or
longer? . .iu
PV=b000 Fv=9iooo raps: M=i2. rrM=l;_ N: WEE] have
MW : [n LESS)
.I‘LS ‘ 33'11? P243045 a: 3,1571%
[HU+“T£) 7t Mau’ci'lﬁ What if you want to buy e boat in 34/2 years? How much must the bank pay with
annual compounding 7 ‘ to make this possible? PV= 600° TIMELINE:
FV: 6000
r:
M: l
N .2: _ x, = _ 3 75 is P“: v
Now we need to rearrange to solve for r. dig}
FV "N _" £92.? [/35 ,1 r "L Fir
"{lwi i in U475 lug ‘ ﬂirt
w '(w 7)
Note that this gives us the annual interest rate. L _ Elly/n I
M ' PU “
’ Fv '
him) l M l, t :n \f
i ‘41 :5; A: 1,)
Y3 I1 \' :'“'.'_ i . _ g [HERN
 ll 1‘3 D  Richard T. Bliss, Baboon University
and Terry D. Nixon, Miami Univmity 49 FIN 301 A,B — Fall 2011 _— .1 Lecture? a; a 51
APR mncLEA a Example 8: You are comparing oneyear investment options. Bank A pays 5.15% APR
iﬁ—m “ compounded monthly, Bank 8, 5.2% APR compounded quarterly.
 ' ‘ 9
APR stands for Annual Percentage Rate which is often the interest rate quoted by Whig '3 meg???“ 93C“ Option
lenders. (5 5“ .11!
What is the EAR of each Option? P U‘l‘ Hoff )m—l 1 5:917:3371 @: rate per period x number of compounding periods per year = rlM X M =© Note that APR is the same as rin our prior problems. .032 \1
‘ (H I). J—l : Joggzgfgﬂ
To make comparisonsrwhen we have different interest rates or compounding frequency. Wh'Ch do you prefer'
we use EAR or theﬁfﬁectﬁW lfhtei;
17> is W Eh!
EAR tells us how much actual cash interest is aid or received. This is what we reall
M QOTE: Once we compute EARS! we have a valid basis fgr comparisonE ' : 2 b t‘ EARS for the two banks.
EAR = (1 + r“mu _ 1 1 El Pragjlce Answer Example ycompu Ing keg S? S ‘“ o .
P APR for annual compounding? [3 3' 2‘!
BAR . may? at as t, M Example 6: The quoted interest rate on your credit ' 
compounding. What is the eﬁ‘ective rate? card IS “25% (APR) With montth Practice: What i s the EAR if Sam offers 12% APR With monthly compounding?
1 ‘1. 10$, e  Richard T. Bliss, Babson umva
. and Tiny D. Nixon, Miami University
©  Richard ‘1‘. Bliss, Babson Univﬂsf'l'
and Terry D, Nixon, Miami Univeﬁﬁl' _
FlN 301A,B  Fall 2011 50 51 FIN 301 A,BFatt 2011
Z" — _ ...
View
Full
Document
 Fall '08
 SCHAEFF
 Annual Percentage Rate, Terry D. Nixon, Richard T. Bliss

Click to edit the document details