HOMEWORK_2_SOLUTION

# HOMEWORK_2_SOLUTION -  Homework ­1Solution ...

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Unformatted text preview:  Homework ­1Solution  1.d)  Quarter1 ­4: ­\$250,000 Quartern:\$40,000(1+0.024)^( 4),n=5,6,...,23 Quarter24:\$40,000((1+0.25)^(20)) \$10,000 1 2. Theamountowedis: ForN=1: F=\$250,000+\$250,000(.073)(1)=\$268,250 ForN=2: F=\$250,000+\$250,000(.073)(2)=\$286,500 ForN=3.5: F=\$250,000+\$250,000(.073)(3.5)=\$313,875 3. Theinterestrateis: i=(\$175,000 \$150,000)/((\$150,000)(4)) =0.0417=4.17%  7.a)  EffectiveMonthlyRate: im=((1+r/M)^lM) 1=(1+(0.095/4)^(4/12) 1=0.0079=0.79%  8.b)  EffectiveQuarterlyRate: iq=(1+r/M)^lM 1=(1+0.08/1)^(1/4) 11=0.0194=1.94%  9.c)  EffectiveQuarterlyInterestRate: iq=e^lr 1=e^((1/4)*0.0745) 1=0.0188=1.88%  10. r=iqM=(0.032)4=0.128=12.8%compoundedquarterly. 14. Definei1=14.3%compoundedsemi ­annuallyandi2=2.1%perquarter. Converteachtoaneffectivesemi ­annualrateforcomparison: i1=0.143/2=0.0715=7.15%persixmonths. i2=(1+0.021)^2=0.0424=4.24%persixmonths. The14.3%compoundedsemi ­annuallyinvestmentisbetter.   20. Monthlyinflationratefmshouldbeconvertedtoannualinflationratef. f=((1+fm)^12) 1=(1+0.0025)^12 1=0.0304=3.04% Realdollars:  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. Quarterlyinflationratefqshouldbeconvertedtoannualinflationratef. f=(1+fq)^4 1=(1+0.0105)^4 1=0.0427=4.27%  Currentdollars: 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.Annualinflation ­freerate: i=(1+i)/(1+f) 1=(1+0.125)/(1+0.025) 1=0.0976=9.76%  ApplicationProblems  3. Amountowedattheendofoneyear: F=P(1+i) \$228,960=12(\$18,000)(1+i) i=0.06=6.0% Theeffectivemonthlyrateis: im=(1+i)^(1/12) 1=(1+0.06)^(1/12) 1=0.00487=0.49%  Iftheywaitfiveyearstopay: F=\$216,000(1+0.06)^5=\$289,056.  6. Definei1=8.5%compoundeddailyandi2=0.75%permonth.Converteachtoaneffective annualrateforcomparison: i1=e^0.085 1=0.0887=8.87%peryear.  i2=(1+0.0075)^12 1=0.0938=9.38%peryear. Asaresult,the8.5%loanischeaper. TheEUR250,000costis\$296,033inU.S.dollarsonDecember30,2005.  8.Thecashflowstreamincurrentdollarsisdefinedbytheactualdollarsreceived: A0= \$10,000 A0.5=\$306.25 A1=\$306.25 ... A8.5=\$306.25 A9=\$10,000+\$306.25 Assuminga2.3%semi ­annualrateofinflation,therealdollarsare:  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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