HW2_Financial_Mathematics_-_Part_3_Solution_Manual

HW2_Financial_Mathematics_-_Part_3_Solution_Manual -...

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SILABO – GERENCIA EMPRESARIAL Universidad Iberoamericana UNIBE Due Date : February 15 2011 Deliver hard copy at the beginning of class. Note: In all the problems set, even though those who involve multiple choices questions, the student must provide a clear mathematical argument for the response. Otherwise a partial credit will be given for correct answers. HOMEWORK 2: Solution Manual CHAPTER 3 Exercise 3.1 24. All of the values in this table are calculated in the same way; the only difference is in the value of the interest rate and number of years. For example, the value in the 6% row and 40 year column would be: FV = PV(1+i)^n $100,000 = PV(1+.06)^40 $100,000 = PV(10.28571794) Divide both sides by the compound interest factor 10.28571794 Page 1 of 35 FINANCIAL MATHEMATICS HOMEWORK 2: PART 3
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PV = $9,722.22 26. FV = PV(1+i)^n $2500 = PV(1+.0597)^2 2500 = PV(1.12296409) Divide both sides by the compound interest factor PV = $2,226.25 28. $2,000 -> $4,000 ->$8,000 -> $16,000 -> $32,000 The money needs to double 4 times. Each doubling will take approximately 72/7.5 = 9.6 years, so 4 doublings will take approximately 4(9.6) = 38.4 years. Since this is an approximately anyway it is reasonable to round the value to 38 years. FV = PV(1+i)^n FV = $2,000(1+.075)^38 FV = $2,000(15.61426844) FV = $31,228.54 30. FV = PV(1+i)^n FV = $3,255.09(1+.0617)^1 FV = $3,255.09(1.0617) FV = $3,455.93 32. FV = PV(1+i)^n FV = ($3,031.95)(1+.0934)^2 FV = $3,031.95(1.19552356) FV = $3,624.77 The interest would be $3,624.77 - $3,031.95 = $592.82 34. Oliver had at the end: FV = PV(1+i)^n FV = $3,500(1+.0625)^4 Page 2 of 35
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FV = $4460.50 So Olivia must have deposited: FV = PV(1+i)^n $4460.50 = PV(1+.0555)^4 4460.50 = PV(1.241174803) PV = $3,593.77 36. “Common sense” suggests that double the interest rate would give you double the future value, but this is not correct. If you look at the comparison table in Exercise 23 for example, you can see this. You can also verify that Ernie wound up with more than $8000 using the rule of 72. Ernie’s account doubled twice in 10 years, so by rule of 72 he earned about 72/4 = 14.4%. At double that rate, 28.8%, Ernie would have ended up with $12,564.89. 38. Rule of 72: 72/4 = 18% FV = PV(1+i)^n FV = $1,000(1+.18)^4 FV = $1,000(1.93877777) $1,938.78 Rule of 70: 70/4 = 17.5% FV = PV(1+i)^n FV = $1,000(1+.175)^4 FV = $1,000(1.9061255391) FV = $1,906.13 Page 3 of 35
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Exercise 3.2 24. Rule of 72: 72/10 = 7.2% approximately (Remember that since Rule of 72 is an approximation and since the difference due to compounding frequency is not huge, it works the same way regardless of compounding frequency.) 26. FV = PV(1+i)^n FV = $32,500(1+.0463/12)^30 FV = $36,480.12 Interest = $36,480.12 - $32,500 = $3,366.59 28. Daily: FV = PV(1+i)^n FV = $1,955.19(1+.06/365)^2555 FV = $2,975.62 Quarterly: FV = PV(1+i)^n FV = $1,955.19(1+.06/4)^28 FV = $2,966.46 Difference: $2,975.62 - $2,966.46 = $9.16 30. We cannot determine the exact number of days, but we can approximate them. Using the rule
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HW2_Financial_Mathematics_-_Part_3_Solution_Manual -...

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