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PresentValueSingleDeposit(Compound)𝐵 = 𝑝 1 + !!

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ContinuousCompounding𝐵 = 𝑝𝑒 !"

FutureValuePeriodicDeposit𝐵 =! !!!!

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PresentValueSingleDeposit𝑝 = !

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PresentValuePeriodicDeposit𝑝 =! !

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1. TheCarpenter’sChroniclecharges$12foreachofthefirstthreelinesofaclassifiedadand$7.25for

eachadditionalline.Expressthecostofanx-linead,c(x),algebraicallyasapiecewisefunction.

2. In1998Lisaearned$149,461.20.TheSocialSecuritymaximumtaxableincomewas$68,400,andtheSocialSecuritypercentwas6.2%.InwhatmonthdidLisahitthemaximumtaxableSocialSecurityincome?HowmuchSocialSecuritytaxdidLisapayinJune,tothenearestcent?

3. Ina’semployeroffersaslidingpaidvacation.Whenshestartedwork,shewasgiventwopaiddaysofvacation.Foreachfour-monthperiodshestaysatthejob,hervacationisincreasedbyoneday.Letxrepresentthenumberof4-monthperiodsworkedandyrepresentthetotalnumberofvacationdays.Writeanequationthatmodelstherelationshipbetweenthesevariables.Howmuchpaidvacationtimewillshehaveafterworkingforthisemployerfor6.5years?

4. Jesseestimatesthatitwillcost$275,000tosendhisnewbornsontoaprivatecollegein18years.Hecurrentlyhas$45,000todepositinanaccount.Whatsimpleinterestratewouldheneedsothat$45,000growsinto$275,000in18years?Roundtothenearestpercent.

5. Ifyouinvested$10,000at3.8%compoundeddailyforfiveyears,whatwouldbeyourendingbalance?

6. KingsParkBankisadvertisingaspecial5.08%APRforCDs.KevintakesoutaoneyearCDfor$24,000.Theinterestiscompoundeddaily.FindtheAPYforKevin’saccount.

7. Ifyoudeposit$3000at2.65%interest,compoundedcontinuously,whatwouldyourendingbalancebeafterfouryears?

8. NickandMattarepartnersinalocalhealthfoodstore.Theyneeded$73,000tostartthebusiness.Theyinvestedintheratio3:7,NicktoMatt.Howmuchmoneydideachinvest?

9. Marilynpurchased2,000sharesofstockfor$25.43pershare.Shesoldthemfor$44.10pershare.Whatwashercapitalgain?

10. Whatwasthepreviousday’scloseforGeneralElectric(G)?

11. Avabought35sharesofstockfor$15persharelastyear.Shepaidherbrokera1%commission.Shesoldthestockthisweekfor$13.25pershare,andpaidherbrokera$30fee.WhatwereAva’snetproceeds?

12. ABCstockwassellingfor$6pershare,withanannualdividendof$.12.Itunderwenta1-for-5reversesplit.Whatwasthevalueofthestockafterthereversesplit?

13. Whatisthedifferencebetweencapitalgain/lossandnetproceeds?

14. Write54 !!%asadecimal.

15. Tonyispayingoffacarloan.Themonthlypaymentis$211.28.Heishopingtoreceiveanincometaxrefundthatislargeenoughtomakeonemonthlypayment.Histaxis$1722andhisemployerwithheld$2071infederaltaxes.WillTonybeabletomakeoncarloanpaymentwiththerefund?Explain.

GE12.5K@26.13!1.13F.67K@5.01"0.38C3K@16.19!1.47T1.6K@26.14"1.08

16. UsingScheduleY-1,writethefirst3linesofapiecewisefunction.

17. UsingScheduleY-1,writeanequationin𝑦 = 𝑚𝑥 + 𝑏formforanincomeover$73,800butnotover$148,850.

18. Evaluatethefunctionforthegivenvalueofx

𝑓 𝑥 = 2𝑥 + 8, 𝑥 ≤ 3𝑥!, 𝑥 > 3

𝑓 3 = 𝑓 6 =

19. OnOctober18DiscoverIncstockclosedat$32.Thecloseonthe17thwas$38.50.Expressthenetchangeasapercent,roundedtothenearesttenth.

20. Sallyhad$8700inmedicalexpenseslastyear.Hermedicalinsurancecovered80%oftheseexpenses.TheIRSallowsmedicalanddentalexpensesdeductionsfortheamountthatexceeds7.5%ofataxpayer’sadjustedgrossincome.IfSally’sadjustedgrossincomeis$20,158,howmuchcansheclaimasamedicaldeduction?Showallworkandexplain.

21. JennandBobaremarriedandfilingseparately.UsingScheduleY-2,calculatetheirtaxforanincomeof$157,173.

22. UsetheTaxRateScheduleformarriedfilingjointtowritealinearequationiny=mx+bformforanincomeover$148,850butnotover$226,850.

23. OnApril23AT&Tclosedat$34.43,whichwasadecreaseof$.72.WhatwasthepercentnetchangefromJune19toJune20forAT&T?Roundtothenearesthundredthofapercent.(Findthe19thclosefirst)

24. Sierrabought500sharesofApple(AAPL)onMarch1at$357.17.TheclosingpriceonApril30was$361.48.Howdidthistradeappearonthestockticker?

25. Aspartoftheiremployeebenefits,allworkersatLightandPowerElectricCompanyreceiveapensionthatiscalculatedbymultiplyingthenumberofyearsworkedtimes1.875%oftheaverageoftheirthreehighestyears’salaries.MiahasworkedforLPECfor30yearsandisretiring.Herhighestsalarieswere$92,000,$94,800,and$96,250.CalculateMia’spension.

26. Mrs.Frasierworkedher40regularhourslastweek,plusfourovertimehoursatthetime-and-a-halfrate.Herhourlyrateis$15.50.HowmuchdidshepayinSocialSecuritytax?

Answers

1. 𝑐 𝑥 = 12𝑥, 0 < 𝑥 ≤ 336 + 7.25(𝑥 − 3), 𝑥 > 3

2. y=2+x;213. June;379.724. 28%5. $12,092.386. 5.21%7. $3335.478. Nick-$21,900

Matt-$51,1009. $37,34010. $2511. $-96.5012. $3013. Captitalgain/lossistheoverallamtmadeorlostinstockandnetproceedstakesfeesintoaccount14. .5462515. 349–Yes,refundislargerthanthepayment

16. 𝑓 𝑥 = .1𝑥, 0 < 𝑥 ≤ 18,1501815 + .15 𝑥 − 18,150 , 18,150 < 𝑥 ≤ 73,800

10,162 + .25 𝑥 − 73,800 , 73,800 < 𝑥 ≤ 148,850

17. 𝑦 = .25𝑥 − 828818. 𝑓 3 = 14 𝑓 6 = 3619. -16.9%20. 228.1521. 39,819.3422. 𝑦 = .28𝑥 − 12,75323. -.2.05%24. 𝐴𝐴𝑃𝐿 500 @ 357.17 ↓ 4.3125. 53,071.8826. 44.21