HOMEWORK_2_SOLUTION

HOMEWORK_2_SOLUTION -  Homework ­1Solution ...

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Unformatted text preview:  Homework ­1Solution  1.d)  Quarter1 ­4: ­$250,000 Quartern:$40,000(1+0.024)^( 4),n=5,6,...,23 Quarter24:$40,000((1+0.25)^(20)) $10,000 1 2. Theamountowedis: ForN=1: F=$250,000+$250,000(.073)(1)=$268,250 ForN=2: F=$250,000+$250,000(.073)(2)=$286,500 ForN=3.5: F=$250,000+$250,000(.073)(3.5)=$313,875 3. Theinterestrateis: i=($175,000 $150,000)/(($150,000)(4)) =0.0417=4.17%  7.a)  EffectiveMonthlyRate: im=((1+r/M)^lM) 1=(1+(0.095/4)^(4/12) 1=0.0079=0.79%  8.b)  EffectiveQuarterlyRate: iq=(1+r/M)^lM 1=(1+0.08/1)^(1/4) 11=0.0194=1.94%  9.c)  EffectiveQuarterlyInterestRate: iq=e^lr 1=e^((1/4)*0.0745) 1=0.0188=1.88%  10. r=iqM=(0.032)4=0.128=12.8%compoundedquarterly. 14. Definei1=14.3%compoundedsemi ­annuallyandi2=2.1%perquarter. Converteachtoaneffectivesemi ­annualrateforcomparison: i1=0.143/2=0.0715=7.15%persixmonths. i2=(1+0.021)^2=0.0424=4.24%persixmonths. The14.3%compoundedsemi ­annuallyinvestmentisbetter.   20. Monthlyinflationratefmshouldbeconvertedtoannualinflationratef. f=((1+fm)^12) 1=(1+0.0025)^12 1=0.0304=3.04% Realdollars:  A'0= ­$280,000/(1+0.0304)^0= ­$280,000 A'1=$200,000/((1+0.0304)^1)=$194,099 A'2=$300,000/((1+0.0304)^2)=$282,559 A'3=$400,000/((1+0.0304)^3)=$365,631 A'4=$500,000/((1+0.0304)^4)=$443,554  A 5=$600,000/((1+0.0304)^5)=$86,094  2 21. Quarterlyinflationratefqshouldbeconvertedtoannualinflationratef. f=(1+fq)^4 1=(1+0.0105)^4 1=0.0427=4.27%  Currentdollars: A1=$120,000(1+0.0427)^1=$125,124 A3=$180,000(1+0.0427)^3=$204,057 A4=$210,000(1+0.0427)^4=$248,231 A5=$250,000(1+0.0427)^5=$308,132  25.Annualinflation ­freerate: i=(1+i)/(1+f) 1=(1+0.125)/(1+0.025) 1=0.0976=9.76%  ApplicationProblems  3. Amountowedattheendofoneyear: F=P(1+i) $228,960=12($18,000)(1+i) i=0.06=6.0% Theeffectivemonthlyrateis: im=(1+i)^(1/12) 1=(1+0.06)^(1/12) 1=0.00487=0.49%  Iftheywaitfiveyearstopay: F=$216,000(1+0.06)^5=$289,056.  6. Definei1=8.5%compoundeddailyandi2=0.75%permonth.Converteachtoaneffective annualrateforcomparison: i1=e^0.085 1=0.0887=8.87%peryear.  i2=(1+0.0075)^12 1=0.0938=9.38%peryear. Asaresult,the8.5%loanischeaper. TheEUR250,000costis$296,033inU.S.dollarsonDecember30,2005.  8.Thecashflowstreamincurrentdollarsisdefinedbytheactualdollarsreceived: A0= $10,000 A0.5=$306.25 A1=$306.25 ... A8.5=$306.25 A9=$10,000+$306.25 Assuminga2.3%semi ­annualrateofinflation,therealdollarsare:  A 0= ­$10,000 A 0.5=$306.25/1.023=%313.29 A 1=$306.25/(1.023^2)=%292.63 . A 8.5=$306.25/(1.023^17)=%208.06 A 9=($10,000+$306.25)/(1.023^18)=%6844.46  3 ...
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