Lecture 2. Tuesday Feb 3 rd. Time Value of Money 1
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1 Lecture 2. Tuesday Feb 3 rd Time Value of Moey 1
2 What is Moey? Moey is a promise A Eglish Bakote says: I promise to pay the Bearer o demad the sum of twety pouds Ad it is siged by the Chief Cashier of the Bak of Eglad Tuesday Feb 3rd Time Value of Moey 1 2
3 What is Moey? Baks got their ame from the Italia Baca meaig a bech A Bakote was the receipt issued for a deposit of precious metals Tuesday Feb 3rd Time Value of Moey 1 3
4 What is Moey? Moey is a cotract betwee the Bearer ad the Bak What you get if you go the Bak of Eglad ad demad twety pouds is ot clear Tuesday Feb 3rd Time Value of Moey 1 4
5 Risk associated with Moey Pouds = Bak of Eglad = British Govermet US Dollars = Federal Reserve = US Govermet 1920 s Germay The year 1923 was oe of crisis for the Weimar Republic (Source: U.S. Library of Cogress) Tuesday Feb 3rd Time Value of Moey 1 5
6 Iflatio i the Weimar Republic The govermet also bega pritig moey at such a rate that it soo became virtually worthless. By the fall of 1923, wheelbarrows were eeded to carry eough currecy for simple purchases. (Source: U.S. Library of Cogress) Tuesday Feb 3rd Time Value of Moey 1 6
7 Iflatio i the Weimar Republic I 1914, US$1 = 4 marks. Bymid-1920, US$1 = 40 marks. By early 1922, US$1 = 200 marks A year later 18,000 marks, ad By November trillio marks. (Source: U.S. Library of Cogress) Tuesday Feb 3rd Time Value of Moey 1 7
8 Movig Moey i Physical Space Try spedig a 20 poud ote to a store i Hadley! Baks will exchage each others promises 20 pouds will get you 36 dollars at curret rates of exchage Tuesday Feb 3rd Time Value of Moey 1 8
9 Movig Moey Forward i Time Uder the mattress I a checkig accout I a savigs accout I a Certificate of Deposit Tuesday Feb 3rd Time Value of Moey 1 9
10 Movig Moey Backward i Time We ca save up to buy a house OR We ca buy the house with moey we do t have, yet Tuesday Feb 3rd Time Value of Moey 1 10
11 Movig Moey i Time $1,000 from Toy Soprao Iterest Rate He will charge a iterest rate of 5 percet per week. At the ed of the week we owe him $1,050 dollars Tuesday Feb 3rd Time Value of Moey 1 11
12 Iterest Iterest is expressed as a percetage of the amout borrowed per period of time Toy s 5 percet per week would be 0.05 (as a decimal fractio) Tuesday Feb 3rd Time Value of Moey 1 12
13 Iterest o Toy s Loa At the ed of the week we would owe Toy $1,050 The Future Value after oe time period $1,000 is the origial amout borrowed The Pricipal or The Preset Value $1,000 * 0.05 = $50 is the iterest Tuesday Feb 3rd Time Value of Moey 1 13
14 Iterest o Toy s Loa - Week 1 $1,050 = $1,000 * 1 + $1,000 * 0.05 Reorgaize the right had side $1,050 = $1,000 * ( ) FV = PV * (1 + Iterest Rate) Tuesday Feb 3rd Time Value of Moey 1 14
15 Iterest o Toy s Loa - Week 1 If we let r represet the variable iterest rate for the period (expressed as a decimal), the We have Formula 3.1 FV = PV 1 + r 1 Tuesday Feb 3rd Time Value of Moey 1 15
16 Iterest o Toy s Loa - Week 2 $1, = $1,050 * 1 + $1,050 * 0.05 $1, = $1,050 * ( ) FV 2 = FV 1 * (1 + r ) Tuesday Feb 3rd Time Value of Moey 1 16
17 Compoud Iterest Iterest is added to the amout at some poit i time Toy s Loa has iterest added every week The iterest rate is five percet per week compoudig weekly Tuesday Feb 3rd Time Value of Moey 1 17
18 Compoud Iterest FV 2 = FV 1 * (1+ r) FV 1 = PV * (1+ r) FV 2 = PV * (1+ r) * (1+ r) FV 2 = PV * (1+ r) 2 Tuesday Feb 3rd Time Value of Moey 1 18
19 Compoud Iterest Periods FV PV ( 1 r) = + This formula allows calculatio of the amout (FV ) that will be owig after time periods startig from a Pricipal (PV) at time zero usig a iterest rate r per period ad compoudig the iterest. Tuesday Feb 3rd Time Value of Moey 1 19
20 Iterest o Toy s Loa - Week 3 Three weeks meas =3 Five percet per week meas r=0.05 Compoudig weekly, so use FV PV ( 1 r) = + PV is still the amout we borrow Tuesday Feb 3rd Time Value of Moey 1 20
21 Iterest o Toy s Loa - Week 3 Slot the values we kow ito the formula ad simplify FV FV FV 3 3 = = 1,000 1,000 ( ) ( 1.05) = 1,000* = 1, Tuesday Feb 3rd Time Value of Moey 1 21
22 Aother Take o The Problem 1 Expect $1,000 i 3 weeks Wat to sped moey ow How much ca we borrow? FV PV ( 1 r) = + Tuesday Feb 3rd Time Value of Moey 1 22
23 Aother Take o The Problem 2 FV FV ( 1 r) PV ( 1 r) = + = PV ( 1+ r) ( 1 r) + + Formula 3.2 FV PV = ( 1 ) + r Tuesday Feb 3rd Time Value of Moey 1 23
24 Newma & The Moey Machie Gives prizes ow (PV) or i the future (FV) Will covert prizes ow (PV) to moey i the future (FV) Will covert prizes i the future (FV) to moey ow (PV) Uses a iterest rate of 10 percet compoudig aually 100% Guaratee so risk free Tuesday Feb 3rd Time Value of Moey 1 24
25 Moey Machie Questio 1 Prize $100 - i 2 years time future (FV) Newma wats moey ow (PV) Machie will trade future prize for moey ow usig 10% iterest rate compoudig aually Tuesday Feb 3rd Time Value of Moey 1 25
26 Moey Machie Questio 1 (PRS) Will Newma get 1. more or 2. less tha $100 ow (PV)? Why? Tuesday Feb 3rd Time Value of Moey 1 26
27 Moey Machie Questio 1 What is the questio askig? We kow After 2 years $100 dollars future (FV) (=2) & FV 2 =$100 Te per cet per aum iterest rate (r=0.10) Tuesday Feb 3rd Time Value of Moey 1 27
28 Moey Machie Questio 1 So use formula 3.2 $100 $100 PV = = ( ) ( ) $100 PV = = $82.64 = FV ( + r) PV 1 Tuesday Feb 3rd Time Value of Moey 1 28
29 Moey Machie Questio 8 Prize $100 - ow (PV) Newma wats moey i 2 years time future (FV) Machie will trade curret prize (PV) for moey i the future (FV) usig 10% iterest rate compoudig aually Tuesday Feb 3rd Time Value of Moey 1 29
30 Moey Machie Questio 8 (PRS) Will Newma get 1. more or 2. less tha $100 i the future (FV) Why? Tuesday Feb 3rd Time Value of Moey 1 30
31 Moey Machie Questio 8 What is the questio askig? We kow $100 dollars ow (PV) (=2) & PV=$100 Te per cet per aum iterest rate (r=0.10) Tuesday Feb 3rd Time Value of Moey 1 31
32 Moey Machie Questio 8 So use formula 3.6 FV PV ( 1 r) = + *( ) 2 FV $ = + FV $100*1.21 $121 2 = = Tuesday Feb 3rd Time Value of Moey 1 32
33 Compoud Iterest Remember we borrowed $1,000 from Toy Soprao at five percet per week compoudig weekly How may weeks will it be before the debt is over $10,000? Tuesday Feb 3rd Time Value of Moey 1 33
34 Compoud Iterest Press 1 for 12 weeks? Press 2 for 24 weeks? Press 3 for 36 weeks? Press 4 for 48 weeks? Press 5 for 60 weeks? Tuesday Feb 3rd Time Value of Moey 1 34
35 Compoud Iterest Iterest O Toy's Loa 15,000 Debt Outstadig 10,000 5,000 10, Weeks Tuesday Feb 3rd Time Value of Moey 1 35
36 Usig a Calculator 2 Formulae FV PV = 1 ( + r) FV PV ( 1 r) = + Both ivolve ( 1 ) +r Use the expoet key Tuesday Feb 3rd Time Value of Moey 1 36
37 Usig a Calculator Iterest rate: Covert percetage to a decimal fractio 10% = 0.10 Add 1 Hit the expoet key ( 1+r) Eter the umber of periods Hit the equals key Tuesday Feb 3rd Time Value of Moey 1 37
38 Usig a Calculator For FV from PV FV Multiply by the PV - doe For Preset Value from Future Value = FV Store result i memory Eter FV = PV 1+ r ( ) Divide by Memory Recall - Doe PV 1 + r ( ) Tuesday Feb 3rd Time Value of Moey 1 38
39 Aoucemets #1 all/ Sed me a with your correct ad curret address adrew.d.hall@verizo.et adhall@som.umass.edu Tuesday Feb 3rd Time Value of Moey 1 39
40 Aoucemets #2 - OWL You should complete the Tutorial by Midight Today OWL Web Page Tuesday Feb 3rd Time Value of Moey 1 40
41 Aoucemets #3 - Surveys o OWL Complete the Surveys o OWL PRS Hadset Number Survey Please complete by ed of today Office Hours Survey (ASAP) Calculator Survey (ASAP) Tuesday Feb 3rd Time Value of Moey 1 41
42 Aoucemets #4 - Calculator Get Oe Start Readig the Maual Experimet with usig it Brig it to every class Check out Course Web Page for help choosig oe ad usig oe Tuesday Feb 3rd Time Value of Moey 1 42
43 Aoucemets #5 - The Course Notes Now available from: CCD $6.25 Tuesday Feb 3rd Time Value of Moey 1 43
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