Module 2 - with solutions(2)

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1、UniversityofConnecticutMath3615:FinancialMathematicsProblems1.Foreachofthefollowingcalculations,theannualeffectiveinterestrateis5%.(a)Whatisthepresentvalueofanannuity-immediateconsistingofapaymentof100attheendofeachyearfor40years?(b)Whatisthepresentvalueofanannuity-immediateconsistingof

2、apaymentof25attheendofeachquarterfor40years?(c)Whatisthepresentvalueofanannuity-immediateconsistingofapaymentof400attheendofeachfourthyearfor40years?(d)Whatisthepresentvalueofanincreasingannuity-immediateconsistingofapaymentof100attheendofthefirstyear,increasingby6eachyearfor40years?(e)

3、Whatisthepresentvalueofageometricannuity-immediateconsistingofapaymentof100attheendofthefirstyear,increasingby6%eachyearfor40years?1.(a)100isdepositedatthebeginningofeachyearfor30years,andearnsapositivelevelcompoundrateofinterest.Thebalanceattheendof30yearsis13timesthebalanceattheendof1

4、5years.Findtheeffectiveannualinterestrate.Findthebalanceattheendof15years.(b)100isdepositedatthebeginningofeachyearfor30years,andearnsapositivelevelcompoundrateofinterest.Thebalanceattheendof30yearsis13timesthebalanceattheendof10years.Findtheeffectiveannualinterestrate.Findthebalanceatt

5、heendof10years.3.A20-yearannuity-immediatehasafirstpaymentof500(payableatt=1).Eachsubsequentpaymentforthenext10yearsincreasesby100,untilapaymentof1500ismadeatt=11.Annualpaymentscontinueat1500untilthefinalpaymentatt=20.Atan8%effectiveannualinterestrate,whatisthepresentvalueofthisannuity?

6、Whatisthevalueattimet=20?4.Youpurchasea1,000parvalue10-yearbondfor1,000.Thebondpayssemi-annualcouponsandhasan8%(annual)couponyield.Youinvestthecouponpaymentsinanaccountthatpays6%annualinterest,convertiblequarterly.Whatisthetotalvalueavailabletoyouattheendof10years?Whatoverallannualeffec

7、tiveinterestratehaveyouearnedduringthe10yearsonyour1,000investment?5.Anarithmeticallyincreasingperpetuity-immediatemakesannualpaymentsof1,2,3,etc.Ageometricperpetuity-immediatemakesannualpaymentsof1,(1.05),(1.05)2,etc.Ifthesetwoperpetuitieshavethesamepresentvalueatanannualeffec