02%20time%20value%20of%20money%20part%201%20test%20bank%20problems%20solutions%202011.02.14%2012.00

02%20time%20value%20of%20money%20part%201%20test%20bank%20problems%20solutions%202011.02.14%2012.00

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FNAN 301 Solutions to test bank problems – time value of money part 1 Some answers may be slightly different than provided solutions due to rounding 1. How much will you have in a. 16 years if you invest $500 today at an annual rate of 5.6%? b. 14 years if you invest $500 today at an annual rate of 5.6%? c. 18 years if you invest $500 today at an annual rate of 5.6%? d. 18 years if you invest $500 today at an annual rate of 6.6%? e. 18 years if you invest $500 today at an annual rate of 4.6%? f. 18 years if you invest $600 today at an annual rate of 4.6%? g. 18 years if you invest $400 today at an annual rate of 4.6%? h. 18 years if you invest $400 today at an annual rate of -4.6%? FV t = C 0 × (1+r) t For all of these problems: Step 1: investment value of several hundred dollars at year 0 and desired amount in 14, 16, or 18 years Step 2A: cash flow can be expressed as taking place in 14, 16, or 18 years and since 14, 16, and 18 are all whole numbers, a year is the largest period from this step Step 2B: no compounding period is given Step 2C: the interest rate that is given is for a year Step 2D: the shortest of the periods identified in steps 2A, 2B, and 2C is a year and is the length that each period on the timeline should reflect Step 3: the rate for a year is the rate that is given a. FV t = C 0 × (1 + r) t C 0 = 500; r = .056; t = 16 FV 16 = 500 × (1.056) 16 = 1,195.62 Mode is not relevant, since PMT = 0 Enter 16 5.6 -500 0 N I% PV PMT FV Solve for 1,195.62 b. FV t = C 0 × (1 + r) t C 0 = 500; r = .056; t = 14 FV 14 = 500 × (1.056) 14 = 1,072.17 Mode is not relevant, since PMT = 0 Enter 14 5.6 -500 0 N I% PV PMT FV Solve for 1,072.17 1
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FNAN 301 Solutions to test bank problems – time value of money part 1 c. FV t = C 0 × (1 + r) t C 0 = 500; r = .056; t = 18 FV 18 = 500 × (1.056) 18 = 1,333.28 Mode is not relevant, since PMT = 0 Enter 18 5.6 -500 0 N I% PV PMT FV Solve for 1,333.28 Note that as the length of time increases, the future value increases, all else equal Note that as the length of time decreases, the future value decreases, all else equal d. FV t = C 0 × (1 + r) t C 0 = 500; r = .066; t = 18 FV 18 = 500 × (1.066) 18 = 1,579.79 Mode is not relevant, since PMT = 0 Enter 18 6.6 -500 0 N I% PV PMT FV Solve for 1,579.79 e. FV t = C 0 × (1 + r) t C 0 = 500; r = .046; t = 18 FV 18 = 500 × (1.046) 18 = 1,123.42 Mode is not relevant, since PMT = 0 Enter 18 4.6 -500 0 N I% PV PMT FV Solve for 1,123.42 Note that as the interest rate or rate of return increases, the future value increases, all else equal Note that as the interest rate or rate of return decreases, the future value decreases, all else equal f. FV t = C 0 × (1 + r) t C 0 = 600; r = .046; t = 18 FV 18 = 600 × (1.046) 18 = 1,348.10 Mode is not relevant, since PMT = 0 Enter 18 4.6 -600 0 N I% PV PMT FV Solve for 1,348.10 2
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FNAN 301 Solutions to test bank problems – time value of money part 1 g. FV t = C 0 × (1 + r) t C 0 = 400; r = .046; t = 18 FV 18 = 400 × (1.046) 18 = 898.73 Mode is not relevant, since PMT = 0 Enter 18 4.6 -400 0 N I% PV PMT FV Solve for 898.73 Note that as the amount invested increases, the future value increases, all else equal Note that as the amount invested decreases, the future value decreases, all else equal h. FV t = C 0 × (1 + r) t C 0 = 400; r = -.046; t = 18 FV 18 = 400 × (1 + (-.046)) 18 = FV 18 = 400 × (.954) 18 = 171.37 Mode is not relevant, since PMT = 0 Enter 18 -4.6 -400 0 N I% PV PMT FV Solve for 171.37 Note that if the rate is negative, then the value of the investment declines over time 3
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FNAN 301 Solutions to test bank problems – time value of money part 1 2. Investment A has a return of RA% per year and investment B has a return of RB% per year.
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