Fle Edit View History Bookmarks Develop Window Help MINDTAP Q Search 05 HW Back
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Fle Edit View History Bookmarks Develop Window Help MINDTAP Q Search 05 HW Back to Assignment Attempts: Do No Harm 36. Problem 5.24 CPresent Valse for Various Discounting Periods) Find the present value of $500 due in the future under each of these conditions 8% nominal rete, semiannual compounding, dsoumed back S years. Do not round intermedate calculations. Round your anser to the nearest ere. a. 337.78 b. 0% nominal rate, quarterty compounding, dscounted back S years. Do not round ntermedate calculations. Round your swer to the nearest s 336.49 c-8% nominal rate, monthly compounding, discounted back 1 year. De not round intermediate cacations. Round your answer to the nearest cent. d. Why do the differences in the PVvs occur? 4 5 WEExplanation / Answer
The formula to calculate the present value of sum due in the future is as under, Present value of sum = F x (1+r)^-n F = Future sum r = rate of interest per compounding period n = number of compounding periods Answer a F = Future sum = $500 r = rate of interest per compounding period = 8%/2 = 4% n = number of compounding periods = 5 years * 2 = 10 Present value of sum = $500 x (1+0.04)^-10 Present value of sum = $337.78 Answer b F = Future sum = $500 r = rate of interest per compounding period = 8%/4 = 0.02 n = number of compounding periods = 5 years * 4 = 20 Present value of sum = $500 x (1+0.02)^-20 Present value of sum = $336.49 Answer c F = Future sum = $500 r = rate of interest per compounding period = 8%/12 = 0.006667 n = number of compounding periods = 5 years * 12 = 60 Present value of sum = $500 x (1+0.006667)^-60 Present value of sum = $335.61 Answer d The difference in the PVs occur as compounding periods per year changes In the above answers , as the compounding periods per year increases the present value declines.
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