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number of periods (i.e., years) for the three different discount rates 6%, 9% and 12%. two changes of 3%, which is kind of like asking us to compare five apples to three oranges) so we’re going to cheat- below is a graph of the PVIF formula vs.
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Interpretation: It’s dangerous to interpret such an a) paucity, and b) disparity of data (i.e., we’re asked to compare the changes due to one change of five years vs. * Differences which are off by 0.001 are due to rounding. Note that, since the future value, $1,000,000, is fixed, all we really need to compare are the Present Value Interest Factors, which are given-calculated with JavaScript using the PVIF formula-in the following table: Present Value Interest Factors and Differences* Savings Bond, which is the PV of $100 at a discount rate of 8% compounded annually for six years, i.e., it must be less than or equal to $100 * 1 / (1+0.08) 6 = $100 * 0.63017 = $63.02.ġ4c) (Paraphrased) Compare the present values of $1,000,000 at 6%, 9%, and 12% APR (compounded annually) after 10 and 15 years comment on the relative impact of interest rate vs. In order to be competitive, it can’t be priced over the present value of the comparable $100 U.S.
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Savings Bond earning 8% APR, compounded annually? Note the text’s description of the problem: Present value concept the referenced concept is that, despite the differences in jargon used, all three of these amounts are the same, namely, the Present Value of $6000 in six years at a discount rate of 12% = $6000 * 1/(1+0.12) 6 = $6000 * 0.507 = $3,042 (using the PVIF from text Table A-2 using the formula gives the more precise result $3,039.79).ġ3) Assuming no cash payments prior to its maturity six years from now, at what current price should a $100 Iowa State bond be sold if it is to be competitive with a similar U.S. Solution: Present Value Interest Factors forįour Pairs of Opportunity Cost and Number of PeriodsĪ) An investment today that will be worth $6000 in six years at 12% APR (compounded annually) ī) The Present Value of $6000 in 6 years at a 12% discount rate Ĭ) The maximum payment today for a promise to receive $6000 in six years at a 12% opportunity cost. * The answer in the back of the book, $15,456, comes from using the FVIF from Table A1-mine is more precise.ĩ) Using the formula given in the text (which gives just the reciprocal of the Future Value Interest Factor), calculate the Present Value Interest Factor for each of the following pairs of opportunity cost and number of periods, and compare with the values given in text Table A-2. We have implemented in JavaScript the formula to calculate \(n\), so we will use that to provide the answers the Reader can confirm these using Table A-1 as instructed.ĭoubling and Quadrupling Times (in years)ĥ) Compare the amounts of interest earned on $1500 after 3, 6, and 9 years at 7% APR, compounded annually.Ĭ) What accounts for the increase in interest earned? One word: compounding.Ħ) (Paraphrased) Find the future value of $14,000 after 5 five years at 2% APR and 4% APR, compounded annually, and the difference between the two.Ī) 2%: $14,000 * (1+0.02) 5 = $15,457.13 * Solution: Future Value Interest Factors forįour Pairs of Interest Rate and Number of Periodsģ) Using text Table A-1, estimate the number of years for an initial investment to a) double and b) quadruple (increase by a factor of four) for the (annual) interest rates given in the Solution Table below. Problem SolutionsĢ) Using the formula given in the text (which we have implemented in file GPVFV.js using JavaScript), calculate the Future Value Interest Factor for each of the following pairs of interest rate and number of periods, and compare with the values given in text Table A-1. Corrections are welcome and should be emailed to a result generated and/or placed by JavaScript. Selected Chapter-End Problem Solutions Chapter 4: Time Value of Money © 2018 by David Lawrence Goldsmith for Note: These solutions are provided as-is, for informational purposes only, with no warranty of any kind, expressed or implied, including that of correctness, adequacy, and/or suitability for any purpose, whatsoever. Principles of Managerial Finance (Brief) 3rd Edition.