Money Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version


 Charla Blankenship
 2 years ago
 Views:
Transcription
1 Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio
2 This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio Foudatio, Chael Oe News ad Ameica Saves. Special thaks to Rudy Gawo fo pepaig the lesso ad to Jill Sulam of Tasfomatios Editig LLC fo editoial guidace. Moey Math fo Tees. Copyight 2014 by the FINRA Ivesto Educatio Foudatio o FINRA Foudatio. Repoductio fo opofit, educatioal puposes is pemitted ad ecouaged. All ights eseved.
3 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest 11th ad 12th Gades Lesso Pla OBJECTIVE Savig ad ivestig moey safely ad wisely ae citical skills fo people of all ages ad backgouds. Amed with the kowledge of how ivestmets wok, savvy ivestos ca make ifomed decisios ad detemie the best ivestmet choices available to them. Studets will: Kow ad be able to use ivestmet vocabulay Kow ad be able to use the fomula fo calculatig compoud iteest Udestad the effect of compoudig o savigs. TEACHING MATERIALS Lesso pla Teache woksheet with pecalculated examples Now You Ty studet woksheet with solutios Studet assessmet woksheet with solutios LESSON ACTIVITY 1. Discuss vocabulay wods picipal, deposit, iteest, tem, APR ad APY. 2. Cetificate of deposit (CD): Compouds aually. Wok though pecalculated examples of aual compoudig (see teache woksheet, Examples 1 ad 2). Example 2 shows compoudig ove multiple yeas. Now You Ty studet woksheet: pactice multiyea aual iteest calculatios (page 10). 3. Statemet savigs accout: Compouds quately. Wok though pecalculated example of quately compoudig (see teache woksheet, Example 3). Note: The calculatios peseted do ot take ito accout that diffeet moths have diffeet umbes of days. Quately calculatios ae doe by computig aual iteest, the dividig by 4. Emphasize that aual iteest paid quately > aual iteest paid aually. Defie ad demostate how to calculate APY. Now You Ty studet woksheet: pactice quately iteest calculatios (page 10). 1 Itoductio
4 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest 4. Compoud iteest fomula: Itoduce the compoud iteest fomula: A = P (1+ ) t Whee: A = Accumulated balace P = Picipal = APR expessed as a decimal = Numbe of compoudig peiods pe yea t = Numbe of yeas the ivestmet lasts Review the sceaio outlied i Example 3, usig the compoud iteest fomula to calculate Michael s picipal, iteest ad APY at the ed of oe yea of quately compoudig. The fomula poduces the same accumulated value ($8,161.20). The iteest is still $ The APY is still 2.015%. Now You Ty studet woksheet: pactice aual vs. quately iteest calculatios usig the compoud iteest fomula (page 11). 5. Moey maket accout: Compouds mothly. Wok though pecalculated example of mothly compoudig (see teache woksheet, Example 4). Note: The calculatios peseted do ot take ito accout that diffeet moths have diffeet umbes of days. Mothly calculatios ae doe by computig aual iteest, the dividig by 12. Recalculate usig the compoud iteest fomula. 6. Aual vs. quately vs. mothly compoudig: If the picipal ad APR of ivestmets that compoud aually, quately ad mothly ae the same, which ivestmet will have the geatest etu i iteest (i.e., APY)? Show that mothly compoudig yields highest APY. Now You Ty studet woksheet: pactice aual, quately ad mothly iteest calculatios usig the compoud iteest fomula (page 12). 7. Discussio: Why might a bak advetise deposit accouts usig APY istead of APR? Why might they advetise APR istead of APY o cedit cads? 8. Evaluate studets compehesio (see assessmet woksheet). 2 Itoductio
5 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Teache Woksheet Vocabulay Picipal: A amout of moey owed by a ivesto ad held by a fiacial istitutio such as a bak. Deposit(s): The act of establishig, o addig to, existig picipal i a accout (veb); the moey placed i the accout (ou). Iteest: The amout of moey you ea by leavig deposits i a bak o fiacial istitutio. Iteest is a pecetage of you picipal. Tem: The peiod of time a ivestmet lasts. Aual pecetage ate (APR): The pecetage ate at which iteest is calculated aually. Cetificate of deposit (CD): A ageemet betwee a ivesto ad a bak (o fiacial istitutio) wheeby the ivesto agees to put a cetai amout of moey o deposit (this is the picipal) fo a cetai amout of time without withdawig it (this is the tem) ad the bak agees to pay the ivesto iteest at a ageedupo pecetage ate, kow as the aual pecetage ate (APR). Compoudig peiod: The amout of time that elapses betwee iteest paymets. Aual compoudig: oce pe yea Quately compoudig: oce evey thee moths Jauay Mach: 1st quate Apil Jue: 2d quate July Septembe: 3d quate Octobe Decembe: 4th quate Mothly compoudig: oce pe moth Compoud iteest: Iteest calculated o both the picipal you have o deposit ad o iteest that has accumulated i the past. 3 Teache Woksheet
6 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Picipal ad Iteest Example 1 Michael is savig moey to buy a ca. He takes $8,0 to the bak ad opes a aual CD upo which the bak agees to pay him 2% iteest. Picipal = 80 Tem = 1 yea APR = 2% = x 0.02 = $ = $8,160 Begiig Balace 2% Iteest Edig Balace $8,0 $160 $8,160 Afte oe yea, Michael has eaed $160 i iteest o his iitial deposit of $8,0, so his balace is ow $8,160. Aual Compoudig: Cetificate of Deposit Example 2 Now, let s say Michael leaves his moey i the bak fo fou yeas. The tem of the aual CD is fou yeas, so he will be eaig 2% iteest pe yea fo fou yeas. Sice this is a aual CD, iteest will be added to the picipal at the ed of evey yea. This is called aual compoudig. Begiig Balace 2% Iteest Edig Balace Yea 1 $8,0. $160. $8,160. Yea 2 $8,160. $ $8, Yea 3 $8, $ $8, Yea 4 $8, $ $8, Teache Woksheet
7 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Quately Compoudig: Statemet Savigs Accout Example 3 Michael s bak offes othe types of ivestmet accouts i additio to cetificates of deposit. Oe such type of accout is a statemet savigs accout. This type of accout is simila to a cetificate of deposit i that it also pays a aual pecetage ate (APR) of iteest, but thee ae some diffeeces, too. A statemet savigs accout does t equie Michael to pomise ot to take the moey out fo a specific peiod of time. Michael ca go i ad withdaw his moey ay time he wats. Also, istead of payig Michael his iteest oly oce pe yea (aually), the bak will make a iteest paymet deposit ito his accout at the ed of evey quate, because statemet savigs accouts compoud quately. Whe the bak makes a iteest paymet, the iteest Michael eaed duig that quate is added to his picipal, ad the ew balace becomes Michael s ew picipal balace fo the ext quate. Now Michael will begi eaig iteest o his iteest! This is called compoud iteest. Let s say Michael takes his $8,0 to the bak ad opes a statemet savigs accout istead of a cetificate of deposit. The bak is goig to pay him the same 2% iteest o this accout that it was offeig fo the CD. Michael s begiig picipal amout is agai $8,0. Also, his APR is still 2%. Howeve, Michael gets iteest compouded quately o this accout. At the ed of the 4th quate, what will Michael s picipal balace be? 1. Fist, calculate his aual iteest: 80 x 0.02 = $ Next, calculate what his 1st quate iteest paymet will be: 160/4 = $40 3. At the ed of the 1st quate, Michael s ew picipal balace will be $8, Next, calculate the aual iteest he will ea o $8,040: 8040 x 0.02 = $ Calculate his 2d quate iteest paymet: /4 = $ At the ed of the 2d quate, Michael s ew picipal balace will be = $8, Next, calculate the aual iteest he will ea o $8,080.20: x 0.02 = $ Calculate his 3d quate iteest paymet: /4 = $ At the ed of the 3d quate, Michael s ew picipal balace will be = $8, Fially, calculate the aual iteest he will ea o $8,120.60: x 0.02 = $ Calculate his 4th quate iteest paymet: /4 = $ At the ed of the 4th quate, Michael s ew picipal balace will be = $8, Afte fou quates have passed, Michael has had his moey i the statemet savigs accout fo oe yea. His edig balace at the ed of that yea is $8, Do you emembe what his edig balace would have bee if he had opeed a aual CD istead? ($8,160) 5 Teache Woksheet
8 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Let s compae these two choices. Which type of accout would have eaed Michael moe iteest? (Statemet savigs accout) How much moe iteest would Michael ea by opeig the statemet savigs accout istead of the aual CD? ($1.20) Why? Afte all, both accouts pay the same 2% APR. If 2% of $8,0 is $160, ad he eaed $ o his picipal i the statemet savigs accout, the he must have actually eaed moe tha 2% i the statemet savigs accout. This is because he eaed iteest o his iteest duig the yea. His statemet savigs accout yielded moe tha 2% fo the yea. This exta eaig because of compoudig iteest is called aual pecetage yield, o APY. APY is the actual ate you moey eas, takig compoudig ito cosideatio. To calculate the APY, we divide the amout of iteest Michael eaed fo the yea by his oigial picipal deposit: APY = = = 2.015% 80 So a statemet savigs accout that pays a APR of 2% will ea a APY of 2.015% because of the effect of compoud iteest. Now You Ty Ask studets to do page 10 of the Now You Ty studet woksheet to pactice calculatig multiyea aual compoud iteest ad quately compoud iteest. 6 Teache Woksheet
9 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Compoud Iteest Fomula As you ca see, compoudig seveal times pe yea ad holdig a ivestmet fo multiple yeas would make fo a lot of maual calculatios. Luckily, thee is a fomula called the compoud iteest fomula that allows us to calculate the accumulated balace of a ivestmet acoss multiple yeas ad multiple compoudig peiods. Itoduce the compoud iteest fomula: A = P (1+ ) t Whee: A = Accumulated balace P = Picipal = APR expessed as a decimal = Numbe of compoudig peiods pe yea t = Numbe of yeas the ivestmet lasts Review the sceaio outlied i Example 3: Let s say Michael takes his $8,0 to the bak ad opes a statemet savigs accout istead of a cetificate of deposit. The bak is goig to pay him the same 2% iteest o this accout that it was offeig fo the CD. Michael s begiig picipal amout is agai $8,0. Also, his APR is still 2%. Howeve, Michael gets iteest compouded quately o this accout. Picipal (P) = 80 A = P (1+ ) t APR () = 2% = = 4 (quately) A = 80(1+ ) 4x1 4 t = 1 yea A = 80( ) 4 A = 80(1.5) 4 A = 80( ) A = $ Compae the iteest calculated usig the fomula with the iteest calculated whe we did the calculatio the log way, by had. Notice that the amout of iteest ($161.20) matches. Now You Ty Ask studets to do page 11 of the Now You Ty studet woksheet. 7 Teache Woksheet
10 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Mothly Compoudig: Moey Maket Savigs Accout Example 4 Michael s bak offes aothe type of ivestmet accout simila to the statemet savigs accout. This accout is called a moey maket savigs accout. This type of accout woks just like a statemet savigs accout except that the compoudig peiod is mothly istead of quately. This meas that Michael will eceive a iteest paymet deposit ito his accout at the ed of evey moth. Whe that happes, the iteest Michael eaed i the pevious moth is added to his picipal, ad the ew balace becomes Michael s ew picipal balace fo the ext moth. So ow Michael will begi eaig iteest o his iteest mothly! This time, Michael takes his $8,0 to the bak ad opes a moey maket savigs accout istead of a statemet savigs accout. The bak is goig to pay him the same 2% o this accout that it was offeig fo the statemet savigs accout. Michael s begiig picipal amout is agai $8,0. Also, his APR is still 2%. Howeve, Michael gets iteest compouded mothly o this accout. Afte thee moths, o oe quate, what will Michael s picipal balace be? 1. Fist, calculate his aual iteest: 80 x 0.02 = $ Next, calculate what his 1st moth s iteest paymet will be: 160/12 = $ At the ed of the 1st moth, Michael s ew picipal balace will be $8, If we cotiue fo all 12 moths of the yea: Begiig Balace 2% Iteest Edig Balace 1st moth $8,0. $13.33 $8, d moth $8, $13.36 $8, d moth $8, $13.38 $8, th moth $8, $13.40 $8, th moth $8, $13.42 $8, th moth $8, $13.44 $8, th moth $8, $13.47 $8, th moth $8, $13.49 $8, th moth $8, $13.51 $8, th moth $8, $13.53 $8, th moth $8, $13.56 $8, th moth $8, $13.58 $8, Note: We ouded up the mothly iteest calculatio befoe we added a moth s iteest to the balace at the begiig of the moth. Thee may be as much as a $0.03 diffeece at the ed of the yea, as ca be see below i the accumulated balace calculated by usig the fomula. This $0.03 diffeece still yields the same APY. 8 Teache Woksheet
11 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Michael s $8,0 oigial picipal deposit, put ito a moey maket savigs accout at 2% APR, compoudig mothly, would be woth $8, at the ed of oe yea. What APY does this accout yield? Agai, divide the amout of iteest Michael eaed fo the yea by his oigial picipal deposit: APY = = = 2.018% 80 Now, let s ty usig the fomula to calculate Michael s balace at the ed of oe yea: Picipal (P) = 80 A = P (1+ ) t APR () = 2% = = 4 (quately) A = 80(1+ ) 12x1 12 t = 1 yea A = 80( ) 12 The fomula yields a accumulated balace of $8, o $0.03 less tha it would be if the calculatio wee doe by had. Compae Aual vs. Quately vs. Mothly Compoudig We ve see that the legth of the compoudig peiod fo a ivestmet affects its APY. If the APR fo a ivestmet is 2%, the APY will be: 2% fo aual compoudig 2.015% fo quately compoudig 2.018% fo mothly compoudig. Now You Ty Ask studets to do page 12 of the Now You Ty studet woksheet. Discussio Questios A = 80(1.1666) 12 A = 80( ) A = $ Why might a bak advetise deposit accouts usig APY istead of APR? Deposit accout iteest eas people moey, so they would be attacted to the highe ate. Why might they advetise APR istead of APY o cedit cads? Cedit cad iteest costs people moey, so they would athe see the lowe ate. Assessmet Ask studets to complete the assessmet woksheet. 9 Teache Woksheet
12 Name Date Studet Woksheet NOW YOU TRY: APR, APY AND COMPOUND INTEREST Aual ad Quately Iteest Taylo wats to ivest he $7,5 college fud at he bak. She picks a aual cetificate of deposit that will pay he 3% iteest each yea. She wo t eed he college moey fo thee moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) A. Fill i the table to fid out how Taylo s ivestmet gows. Begiig Balace 3% Iteest Edig Balace Yea 1 $7,5. Yea 2 Yea 3 B. If Taylo chose a statemet savigs accout that compouds quately istead, how would he accout gow i the fist yea? Begiig Balace 3% Iteest Edig Balace 1st quate $7,5. 2d quate 3d quate 4th quate C. Compae the APYs Taylo s accouts would ea depedig o which accout type she chooses. Aual CD APY: Quately statemet savigs accout APY: 10 Studet Woksheet
13 Name Date Aual vs. Quately Iteest: Compoud Iteest Fomula Thee is a fomula you ca use to calculate the edig balace of a ivestmet if you kow cetai facts about the ivestmet, such as its picipal, APR, compoudig peiods ad the umbe of yeas the ivestmet lasts. A = P (1+ ) t Whee: A = Accumulated balace P = Picipal = APR expessed as a decimal = Numbe of compoudig peiods pe yea t = Numbe of yeas the ivestmet lasts Let s look agai at Taylo s situatio: Taylo wats to ivest he $7,5 college fud at he bak. She has two ivestmet optios: a CD that compouds aually, o a statemet savigs accout that compouds quately. Both ae offeig a APR of 3%. She wo t eed he college moey fo thee moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) 2. What ae the Picipal = APR = Numbe of compoudig peiods pe yea = Numbe of yeas the ivestmet lasts = 3 fo the CD ad the statemet savigs accout? Use the compoud iteest fomula to calculate he balace at the ed of the theeyea ivestmet peiod fo both the aual CD ad the quately statemet savigs accout. Aual CD A = P (1+ ) t A = P (1+ ) t Quately Statemet Savigs Accout 11 Studet Woksheet
14 Name Date Aual vs. Quately vs. Mothly Iteest: Compoud Iteest Fomula Adea wats to ivest $2,5 at he bak. She has thee ivestmet optios: a CD that compouds aually, a statemet savigs accout that compouds quately o a moey maket savigs accout that compouds mothly. All ae offeig a APR of 3%. She wo t eed the fuds i he accout fo five moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) A. Use the compoud iteest fomula to calculate he balace at the ed of the fiveyea ivestmet peiod fo each optio: the aual CD, quately statemet savigs accout ad mothly moey maket savigs accout. A = P (1+ ) t Aual CD Quately Statemet Savigs Accout Mothly Moey Maket Savigs Accout B. Explai what ivestmet advice you d give Adea ad why. 12 Studet Woksheet
15 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Studet Woksheet: Solutios NOW YOU TRY: SOLUTIONS Aual ad Quately Iteest 1. Taylo wats to ivest he $7,5 college fud at he bak. She picks a aual cetificate of deposit that will pay he 3% iteest each yea. She wo t eed he college moey fo thee moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) A. Fill i the table to fid out how Taylo s ivestmet gows. Begiig Balace 3% Iteest Edig Balace Yea 1 $7,5. $225. $7,725. Yea 2 $7,725. $ $7, Yea 3 $7, $ $8, B. If Taylo chose a statemet savigs accout that compouds quately istead, how would he accout gow i the fist yea? Begiig Balace 3% Iteest Edig Balace 1st quate $ 7,5. $56.25 $7, d quate $7, $56.67 $7, d quate $7, $57.10 $7, th quate $7, $57.53 $7, C. Compae the APYs Taylo s accouts would ea depedig o which accout type she chooses. Aual CD APY: 225 APY = = 0.03 = 3% 75 Quately statemet savigs accout APY: APY = = = 3.034% Studet Woksheet: Solutios
16 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Aual vs. Quately Iteest: Compoud Iteest Fomula Thee is a fomula you ca use to calculate the edig balace of a ivestmet if you kow cetai facts about the ivestmet, such as its picipal, APR, compoudig peiods ad the umbe of yeas the ivestmet lasts. Whee: A = Accumulated balace A = P (1+ ) t P = Picipal = APR expessed as a decimal = Numbe of compoudig peiods pe yea t = Numbe of yeas the ivestmet lasts Let s look agai at Taylo s situatio: Taylo wats to ivest he $7,5 college fud at he bak. She has two ivestmet optios: a CD that compouds aually, o a statemet savigs accout that compouds quately. Both ae offeig a APR of 3%. She wo t eed he college moey fo thee moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) 2. What ae the Picipal = 75 APR = 3% = 0.03 Numbe of compoudig peiods pe yea = 1 fo the CD, 4 fo the statemet savigs accout Numbe of yeas the ivestmet lasts = 3 fo the CD ad the statemet savigs accout? Use the compoud iteest fomula to calculate he balace at the ed of the theeyea ivestmet peiod fo both the aual CD ad the quately statemet savigs accout. Aual CD A = P (1+ ) t 0.03 A = 75(1+ 1 A = 75(1.03) 3 A = 75( ) A = $ ) 1x3 Quately Statemet Savigs Accout A = P (1+ ) t 0.03 A = 75(1+ ) 4x3 4 A = 75( ) 12 A = 75(1.75) 12 A = 75( ) A = $ Studet Woksheet: Solutios
17 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Aual vs. Quately vs. Mothly Iteest: Compoud Iteest Fomula 3. Adea wats to ivest $2,5 at he bak. She has thee ivestmet optios: a CD that compouds aually, a statemet savigs accout that compouds quately o a moey maket savigs accout that compouds mothly. All ae offeig a APR of 3%. She wo t eed the fuds i he accout fo five moe yeas. (Remembe, 3% is 0.03 whe witte as a decimal.) A. Use the compoud iteest fomula to calculate he balace at the ed of the fiveyea ivestmet peiod fo each optio: the aual CD, quately statemet savigs accout ad mothly moey maket savigs accout. A = P (1+ ) t Aual CD Quately Statemet Mothly Savigs Accout Moey Maket Savigs Accout 0.03 A = 25(1+ 1 A = 25(1.03) 5 A = 25( ) A = $2, ) 1x A = 25(1+ ) 4x5 4 A = 25( ) 20 A = 25(1.75) 20 A = 25( ) A = $2, A = 25(1+ 12 A = 25( ) 60 A = 25(1.25) 60 A = 25( ) A = $2, ) 12x5 B. Explai what ivestmet advice you d give Adea ad why. Adea should put he moey ito the moey maket savigs accout that compouds mothly because it will yield the geatest etu. 15 Studet Woksheet: Solutios
18 Name Date Studet Assessmet Savig moey ad plaig fo you futue ae ot oly smat thigs to do, they e essetial! Makig smat decisios about ivestmets begis by educatig youself about what types of ivestmets ae available to you ad which will wok the best fo you i you paticula situatio. The compoud iteest fomula is a tool you ca use to evaluate diffeet ivestmets. Make it wok fo you. A = P (1+ ) t Goal: You wat to have $10,0 saved i a fiveyea time fame. How much picipal would you eed to put away i a bak accout offeig a 4% APR ad compoudig mothly i ode to each that goal? A = P = = = t = Challege You have $8,250 to ivest, ad you wo t eed the moey util five yeas fom ow. You decide you will put the moey ito a bak accout compoudig mothly fo that peiod of time. If you goal is to have $10,0 whe the ivestmet matues, what APR do you eed to achieve you goal? A = P = = = t = 16 Studet Assessmet
19 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest Studet Assessmet: Solutios Savig moey ad plaig fo you futue ae ot oly smat thigs to do, they e essetial! Makig smat decisios about ivestmets begis by educatig youself about what types of ivestmets ae available to you ad which will wok the best fo you i you paticula situatio. The compoud iteest fomula is a tool you ca use to evaluate diffeet ivestmets. Make it wok fo you. A = P (1+ ) t Goal: You wat to have $10,0 saved i a fiveyea time fame. How much picipal would you eed to put away i a bak accout offeig a 4% APR ad compoudig mothly i ode to each that goal? A = 1 P = ukow = 4% = 0.04 = 12 t = = P (1+ ) 12x = P (1.333) 60 1 = P ( ) 1 P = = $8, You d have to ivest $8, to accumulate $10,0 five yeas fom ow. Challege You have $8,250 to ivest, ad you wo t eed the moey util five yeas fom ow. You decide you will put the moey ito a bak accout compoudig mothly fo that peiod of time. If you goal is to have $10,0 whe the ivestmet matues, what APR do you eed to achieve you goal? A = 1 P = 8250 = ukow = 12 t = 5 17 Studet Assessmet: Solutios
20 Itoductio to Eaig Iteest: APR, APY ad Compoud Iteest 60 1 = 8250(1+ ) 12x = (1+ ) =(1+ ) = 60 (1+ ) 60 =(1+ ) =(1+ ) = x 12 = = = % You d eed the accout to have a APR of % to accumulate $10,0 five yeas fom ow. 18 Studet Assessmet: Solutios
Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions
Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isketu tadeoff ad time value of
More informationFinance Practice Problems
Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.
More informationAnnuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments
8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 21 22 Leaig
More informationPresent Value Factor To bring one dollar in the future back to present, one uses the Present Value Factor (PVF): Concept 9: Present Value
Cocept 9: Preset Value Is the value of a dollar received today the same as received a year from today? A dollar today is worth more tha a dollar tomorrow because of iflatio, opportuity cost, ad risk Brigig
More informationFM4 CREDIT AND BORROWING
FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer
More informationCHAPTER 11 Financial mathematics
CHAPTER 11 Fiacial mathematics I this chapter you will: Calculate iterest usig the simple iterest formula ( ) Use the simple iterest formula to calculate the pricipal (P) Use the simple iterest formula
More informationANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... 2 WHAT IS AN ANNUITY?... 2 EXAMPLE 1... 2 QUESTIONS...
ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS ANNUITIES SOFTWARE ASSIGNMENT TABLE OF CONTENTS... 1 ANNUITIES SOFTWARE ASSIGNMENT... WHAT IS AN ANNUITY?... EXAMPLE 1... QUESTIONS... EXAMPLE BRANDON S
More informationChecklist. Assignment
Checklist Part I Fid the simple iterest o a pricipal. Fid a compouded iterest o a pricipal. Part II Use the compoud iterest formula. Compare iterest growth rates. Cotiuous compoudig. (Math 1030) M 1030
More informationFI A CIAL MATHEMATICS
CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123
More informationHow to use what you OWN to reduce what you OWE
How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other shortterm assets ito chequig ad savigs accouts.
More information.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
More informationTime Value of Money. First some technical stuff. HP10B II users
Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle
More informationMMQ Problems Solutions with Calculators. Managerial Finance
MMQ Problems Solutios with Calculators Maagerial Fiace 2008 Adrew Hall. MMQ Solutios With Calculators. Page 1 MMQ 1: Suppose Newma s spi lads o the prize of $100 to be collected i exactly 2 years, but
More informationCDs Bought at a Bank verses CD s Bought from a Brokerage. Floyd Vest
CDs Bought at a Bak verses CD s Bought from a Brokerage Floyd Vest CDs bought at a bak. CD stads for Certificate of Deposit with the CD origiatig i a FDIC isured bak so that the CD is isured by the Uited
More information5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationSimple Annuities Present Value.
Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX9850GB PLUS to efficietly compute values associated with preset value auities.
More informationI. Why is there a time value to money (TVM)?
Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios
More informationBreakeven Holding Periods for Tax Advantaged Savings Accounts with Early Withdrawal Penalties
Beakeve Holdig Peiods fo Tax Advataged Savigs Accouts with Ealy Withdawal Pealties Stephe M. Hoa Depatmet of Fiace St. Boavetue Uivesity St. Boavetue, New Yok 4778 Phoe: 76375209 Fax: 7637529 email:
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationPENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.
PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.
More informationA Resource for Freestanding Mathematics Qualifications Working with %
Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%
More informationBINOMIAL THEOREM. 1. Introduction. 2. The Binomial Coefficients. ( x + 1), we get. and. When we expand
BINOMIAL THEOREM Itoductio Whe we epad ( + ) ad ( + ), we get ad ( + ) = ( + )( + ) = + + + = + + ( + ) = ( + )( + ) = ( + )( + + ) = + + + + + = + + + 4 5 espectively Howeve, whe we ty to epad ( + ) ad
More informationCONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationFI3300 Corporate Finance
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multipeiod multicf timevalueofmoney poblems: Geneal case Pepetuity
More information2 Time Value of Money
2 Time Value of Moey BASIC CONCEPTS AND FORMULAE 1. Time Value of Moey It meas moey has time value. A rupee today is more valuable tha a rupee a year hece. We use rate of iterest to express the time value
More informationLearning objectives. Duc K. Nguyen  Corporate Finance 21/10/2014
1 Lecture 3 Time Value of Moey ad Project Valuatio The timelie Three rules of time travels NPV of a stream of cash flows Perpetuities, auities ad other special cases Learig objectives 2 Uderstad the timevalue
More informationDerivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
More informationSolving Logarithms and Exponential Equations
Solvig Logarithms ad Epoetial Equatios Logarithmic Equatios There are two major ideas required whe solvig Logarithmic Equatios. The first is the Defiitio of a Logarithm. You may recall from a earlier topic:
More informationTerminology for Bonds and Loans
³ ² ± Termiology for Bods ad Loas Pricipal give to borrower whe loa is made Simple loa: pricipal plus iterest repaid at oe date Fixedpaymet loa: series of (ofte equal) repaymets Bod is issued at some
More informationHow to set up your GMC Online account
How to set up your GMC Olie accout Mai title Itroductio GMC Olie is a secure part of our website that allows you to maage your registratio with us. Over 100,000 doctors already use GMC Olie. We wat every
More informationSavings and Retirement Benefits
60 Baltimore Couty Public Schools offers you several ways to begi savig moey through payroll deductios. Defied Beefit Pesio Pla Tax Sheltered Auities ad Custodial Accouts Defied Beefit Pesio Pla Did you
More informationTHE TIME VALUE OF MONEY
QRMC04 9/17/01 4:43 PM Page 51 CHAPTER FOUR THE TIME VALUE OF MONEY 4.1 INTRODUCTION AND FUTURE VALUE The perspective ad the orgaizatio of this chapter differs from that of chapters 2 ad 3 i that topics
More informationTO: Users of the ACTEX Review Seminar on DVD for SOA Exam FM/CAS Exam 2
TO: Users of the ACTEX Review Semiar o DVD for SOA Exam FM/CAS Exam FROM: Richard L. (Dick) Lodo, FSA Dear Studets, Thak you for purchasig the DVD recordig of the ACTEX Review Semiar for SOA Exam FM (CAS
More informationVALUATION OF FINANCIAL ASSETS
P A R T T W O As a parter for Erst & Youg, a atioal accoutig ad cosultig firm, Do Erickso is i charge of the busiess valuatio practice for the firm s Southwest regio. Erickso s sigle job for the firm is
More informationINVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
More informationEnhance Your Financial Legacy Variable Annuities with Death Benefits from Pacific Life
Ehace Your Fiacial Legacy Variable Auities with Death Beefits from Pacific Life 9/15 2018815C FOR CALIFORNIA As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three
More informationPeriodic Review Probabilistic MultiItem Inventory System with Zero Lead Time under Constraints and Varying Order Cost
Ameica Joual of Applied Scieces (8: 37, 005 ISS 546939 005 Sciece Publicatios Peiodic Review Pobabilistic MultiItem Ivetoy System with Zeo Lead Time ude Costaits ad Vayig Ode Cost Hala A. Fegay Lectue
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationRepeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
More informationEnhance Your Financial Legacy Variable Annuity Death Benefits from Pacific Life
Ehace Your Fiacial Legacy Variable Auity Death Beefits from Pacific Life 7/15 2017215B As You Pla for Retiremet, Protect Your Loved Oes A Pacific Life variable auity ca offer three death beefits that
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More informationManaging Your Money. UNIT 4D Loan Payments, Credit Cards, and Mortgages: We calculate monthly payments and explore loan issues.
A fool ad his moey are soo parted. Eglish proverb Maagig Your Moey Maagig your persoal fiaces is a complex task i the moder world. If you are like most Americas, you already have a bak accout ad at least
More informationI apply to subscribe for a Stocks & Shares ISA for the tax year 20 /20 and each subsequent year until further notice.
IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form IFSL Brooks Macdoald Fud Stocks & Shares ISA Trasfer Applicatio Form Please complete usig BLOCK CAPITALS ad retur the completed form
More informationMoney Math for Teens. Introduction to Earning Interest: Middle School Version
Money Math for Teens Introduction to Earning Interest: Middle School Version This Money Math for Teens lesson is part of a series created by Generation Money, a multimedia financial literacy initiative
More informationAmendments to employer debt Regulations
March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios
More informationTime Value of Money, NPV and IRR equation solving with the TI86
Time Value of Moey NPV ad IRR Equatio Solvig with the TI86 (may work with TI85) (similar process works with TI83, TI83 Plus ad may work with TI82) Time Value of Moey, NPV ad IRR equatio solvig with
More informationInformation about Bankruptcy
Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationCHAPTER 4: NET PRESENT VALUE
EMBA 807 Corporate Fiace Dr. Rodey Boehe CHAPTER 4: NET PRESENT VALUE (Assiged probles are, 2, 7, 8,, 6, 23, 25, 28, 29, 3, 33, 36, 4, 42, 46, 50, ad 52) The title of this chapter ay be Net Preset Value,
More informationINTRODUCTION TO ENGINEERING ECONOMICS. Types of Interest
INTRODUCTION TO ENGINEERING ECONOMICS A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig by Dr. Ibrahim A. Assakkaf Sprig 2000 Departmet of Civil ad Evirometal Egieerig Uiversity
More informationCurrent Year Income Assessment Form
Curret Year Icome Assessmet Form Academic Year 2015/16 Persoal details Perso 1 Your Customer Referece Number Your Customer Referece Number Name Name Date of birth Address / / Date of birth / / Address
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationBENEFITCOST ANALYSIS Financial and Economic Appraisal using Spreadsheets
BENEITCST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal  Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationHow to read A Mutual Fund shareholder report
Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.
More informationGrow your business with savings and debt management solutions
Grow your busiess with savigs ad debt maagemet solutios A few great reasos to provide bak ad trust products to your cliets You have the expertise to help your cliets get the best rates ad most competitive
More informationTwo people, one policy. Affordable longterm care coverage for both.
Logterm care rider, available o Natiowide YourLife NoLapse Guaratee SUL II Feature guide LIFE INSURANCE + LONGERM CARE wo people, oe policy. Affordable logterm care coverage for both. NAIONWIDE LIFE
More informationECE 340 Lecture 13 : Optical Absorption and Luminescence 2/19/14 ( ) Class Outline: Band Bending Optical Absorption
/9/4 ECE 34 Lectue 3 : Optical Absoptio ad Lumiescece Class Outlie: Thigs you should kow whe you leave Key Questios How do I calculate kietic ad potetial eegy fom the bads? What is diect ecombiatio? How
More informationFramingham State College Department of Economics and Business Managerial Finance Practice Final Exam Spring 2006
Name Framigham State College Departmet of Ecoomics ad Busiess Maagerial Fiace Practice Fial Exam Sprig 2006 This exam provides questios that are represetative of those cotaied o your exam. This test should
More informationGet advice now. Are you worried about your mortgage? New edition
New editio Jauary 2009 Are you worried about your mortgage? Get advice ow If you are strugglig to pay your mortgage, or you thik it will be difficult to pay more whe your fixedrate deal eds, act ow to
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationFor customers Key features of the Guaranteed Pension Annuity
For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether
More informationFlexible Trust. (Settlor as trustee with optional survivorship clause) Your questions answered. What is a trust? What is a Flexible Trust?
Flexible Trust (Settl as trustee with optioal survivship clause) Your questios aswered Uderstadig trusts ad their implicatios ca be pretty complicated. You should always get advice from your legal adviser
More information1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : pvalue
More informationHow deductible plans work
Idividual ad Family Plas DEDUCTIBLE PLANS How deductible plas work Deductible plas geerally offer lower mothly premiums i exchage for payig more out of your ow pocket for services covered by your health
More informationMy first gold holdings. My first bank. Simple. Transparent. Individual. Our investment solutions for clients abroad.
My first gold holdigs. My first bak. Simple. Trasparet. Idividual. Our ivestmet solutios for cliets abroad. The perfect basis for workig together successfully The wheel of time is turig faster tha ever
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationwhere: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return
EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The
More informationExponential function: For a > 0, the exponential function with base a is defined by. f(x) = a x
MATH 11011 EXPONENTIAL FUNCTIONS KSU AND THEIR APPLICATIONS Defiitios: Expoetial fuctio: For a > 0, the expoetial fuctio with base a is defied by fx) = a x Horizotal asymptote: The lie y = c is a horizotal
More informationBasic Elements of Arithmetic Sequences and Series
MA40S PRECALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic
More informationA Podiatrists Guide to Earning More, Working Less and Enjoying What You Do Each Day. Tyson E. Franklin
A Podiatrists Guide to Earig More, Workig Less ad Ejoyig What You Do Each Day Tyso E. Frakli MOVING OUT OF YOUR COMFORT ZONE 1Years ago, if someoe had told me I d be livig i Cairs oe day I would have laughed.
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationI apply to subscribe for a Stocks & Shares NISA for the tax year 2015/2016 and each subsequent year until further notice.
IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form IFSL Brooks Macdoald Fud Stocks & Shares NISA trasfer applicatio form Please complete usig BLOCK CAPITALS ad retur the completed form
More informationPage 1. Real Options for Engineering Systems. What are we up to? Today s agenda. J1: Real Options for Engineering Systems. Richard de Neufville
Real Optios for Egieerig Systems J: Real Optios for Egieerig Systems By (MIT) Stefa Scholtes (CU) Course website: http://msl.mit.edu/cmi/ardet_2002 Stefa Scholtes Judge Istitute of Maagemet, CU Slide What
More informationDC College Savings Plan Helping Children Reach a Higher Potential
529 DC College Savigs Pla Helpig Childre Reach a Higher Potetial reach Sposored by Govermet of the District of Columbia Office of the Mayor Office of the Chief Fiacial Officer Office of Fiace ad Treasury
More informationSolving Inequalities
Solvig Iequalities Say Thaks to the Authors Click http://www.ck12.org/saythaks (No sig i required) To access a customizable versio of this book, as well as other iteractive cotet, visit www.ck12.org CK12
More informationPFF2 2015/16. Assessment of Financial Circumstances For parents and partners of students. /SFEngland. /SF_England SFE/PFF2/1516/B
PFF2 2015/16 Assessmet of Fiacial Circumstaces For parets ad parters of studets SFE/PFF2/1516/B /SF_Eglad /SFEglad Who should complete this form? Complete this form if you are: The studet s atural or adoptive
More informationReview for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that
More informationPreSuit Collection Strategies
PreSuit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process
More informationQuestion 2: How is a loan amortized?
Questio 2: How is a loa amortized? Decreasig auities may be used i auto or home loas. I these types of loas, some amout of moey is borrowed. Fixed paymets are made to pay off the loa as well as ay accrued
More informationMathematical goals. Starting points. Materials required. Time needed
Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios
More informationHandling. Collection Calls
Hadlig the Collectio Calls We do everythig we ca to stop collectio calls; however, i the early part of our represetatio, you ca expect some of these calls to cotiue. We uderstad that the first few moths
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationTrusteed IRAs. Integrate and simplify your retirement and estate plans
Trusteed IRAs Itegrate ad simplify your retiremet ad estate plas Trusteed IRAs from Merrill Lych Trust Compay To create the legacy of your dreams, you may eed more tha a Idividual Retiremet Accout ad a
More informationTwo degree of freedom systems. Equations of motion for forced vibration Free vibration analysis of an undamped system
wo degee of feedom systems Equatios of motio fo foced vibatio Fee vibatio aalysis of a udamped system Itoductio Systems that equie two idepedet d coodiates to descibe thei motio ae called two degee of
More informationStatement of cash flows
6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets
More informationTenants handbook Booklet 4. Paying your rent. June 2015
Teats hadbook Booklet 4 Payig your ret Jue 2015 Your Ret ad other charges Payig your ret ad other charges is a coditio of your teacy. If you do ot pay, you will have broke your teacy agreemet with us.
More informationTIAACREF Wealth Management. Personalized, objective financial advice for every stage of life
TIAACREF Wealth Maagemet Persoalized, objective fiacial advice for every stage of life A persoalized team approach for a trusted lifelog relatioship No matter who you are, you ca t be a expert i all aspects
More informationProfessional Networking
Professioal Networkig 1. Lear from people who ve bee where you are. Oe of your best resources for etworkig is alumi from your school. They ve take the classes you have take, they have bee o the job market
More informationSTATISTICS: MODULE 12122. Chapter 3  Bivariate or joint probability distributions
STATISTICS: MODULE Chapte  Bivaiate o joit pobabilit distibutios I this chapte we coside the distibutio of two adom vaiables whee both adom vaiables ae discete (cosideed fist) ad pobabl moe impotatl whee
More informationINCOME PROTECTION POLICY CONDITIONS GUARANTEED PREMIUMS
INCOME PROTECTION POLICY CONDITIONS GUARANTEED PREMIUMS Documet referece: MIMIIP12G This is a imptat documet Please keep it i a safe place. Icome Protectio Guarateed Premiums Policy Coditios Welcome to
More informationWE KEEP GOOD COMPANY REVITALIZING STORES FOR BIG BRAND FRANCHISES CFG. Recapitalization. Growth Capital CAROLINA FINANCIAL GROUP
REVITALIZING STORES FOR BIG BRAND FRANCHISES Recapitalizatio Frachise ad Restaurats Growth Capital I ve spet my career buildig valuable restaurat frachises for some of the top QSR brads i America. We eeded
More informationIntroducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.
Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easytoread statemet. It provides a overview of your accout ad a complete
More informationOn the Optimality and Interconnection of Valiant LoadBalancing Networks
O the Optimality ad Itecoectio of Valiat LoadBalacig Netwoks Moshe Babaioff ad Joh Chuag School of Ifomatio Uivesity of Califoia at Bekeley Bekeley, Califoia 94720 4600 {moshe,chuag}@sims.bekeley.edu
More informationTime Value of Money and Investment Analysis
Time Value of Moey ad Ivestmet Aalysis Explaatios ad Spreadsheet Applicatios for Agricultural ad Agribusiess Firms Part I. by Bruce J. Sherrick Paul N. Elliger David A. Lis V 1.2, September 2000 The Ceter
More informationLiteral Equations and Formulas
. Literal Equatios ad Formulas. OBJECTIVE 1. Solve a literal equatio for a specified variable May problems i algebra require the use of formulas for their solutio. Formulas are simply equatios that express
More informationSum of Exterior Angles of Polygons TEACHER NOTES
Sum of Exterior Agles of Polygos TEACHER NOTES Math Objectives Studets will determie that the iterior agle of a polygo ad a exterior agle of a polygo form a liear pair (i.e., the two agles are supplemetary).
More information