dachen2007118963_2

# dachen2007118963_2 - Chapter 4 Time Value of Money E4-2....

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Chapter 4 Time Value of Money E4-2. Finding the Future Value Answer: Since the interest is compounded monthly, the number of periods is 4 × 12 = 48 and the monthly interest rate is 1/12th of the annual rate. FV 48 = PV × (1 + i) 48 where i is the monthly interest rate i = 0.02 ÷ 12 = 0.00166667 FV 48 = (\$1,260 + \$975) × (1 + 0.00166667) 48 FV 48 = (\$1,260 + \$975) × (1 + 0.00166667) 48 FV 48 = (\$2,235) × 1.083215 = \$2,420.99 If using a financial calculator, set the calculator to 12 compounding periods per year and input the following: PV = \$2,235 I/year = 2 N = 48 (months) Solve for FV FV = \$2,420.99 Note: Not all financial calculators work in the same manner. Some require the user to use the CPT (Compute) button. Others require the user to calculate the monthly interest rate and input that amount rather than the annual rate. The steps shown in the solution manual will be the inputs needed to use the Hewlett Packard 10B or 10BII models. If using a spreadsheet, the solution is: Column A Column B Cell 1 Future Value of a Single Amount Cell 2 Present Value \$2,235 Cell 3 Interest rate, pct per year compounded monthly = 2/12 Cell 4 Number of months = 4 × 12 Cell 5 Future Value = FV(B3,B4,0,–B2,0) Cell B5 = \$2,420.99 E4-6. Determining Deposits Needed to Accumulate a Future Sum Answer: The financial calculator input is as follows: FV = –\$150,000 N = 18 I = 6% Solve for PMT. PMT = \$4,853.48

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Chapter 4 Time Value of Money 74 ± Solutions to Problems P4-2. LG 2: Future Value Calculation: FV n = PV × (1 + i) n Basic Case A FVIF 12%,2 periods = (1 + 0.12) 2 = 1.254 B FVIF 6%,3 periods = (1 + 0.06) 3 = 1.191 C FVIF 9%,2 periods = (1 + 0.09) 2 = 1.188 D FVIF 3%,4 periods = (1 + 0.03) 4 = 1.126 P4-6. LG 2: Time Value Challenge (a) ( 1) FV 5 = PV × (FVIF 2%,5 ) (2) FV 5 = PV × (FVIF 4%,5 ) FV 5 = \$14,000 × (1.104) FV 5 = \$14,000 × (1.217) FV 5 = \$15,456.00 FV 5 = \$17,038.00 Calculator solution: \$15,457.13 Calculator solution: \$17,033.14 (b) The car will cost \$1,582 more with a 4% inflation rate than an inflation rate of 2%. This increase is 10.2% more (\$1,582 ÷ \$15,456) than would be paid with only a 2% rate of inflation. P4-8. LG 2: Time Value: FV n = PV × FVIF i%,n Challenge (a) \$15,000 = \$10,200 × FVIF i%,5 (b) \$15,000 = \$8,150 × FVIF i%,5 FVIF i%,5 = \$15,000 ÷ \$10,200 = 1.471 FVIF i%,5 = \$15,000 ÷ \$8,150 = 1.840 8% < i < 9% 12% < i < 13% Calculator Solution: 8.02% Calculator Solution: 12.98% (c) \$15,000 = \$7,150 × FVIF i%,5 FVIF i%,5 = \$15,000 ÷ \$7,150 = 2.098 15% < i < 16% Calculator Solution: 15.97% P4-10. LG 2: Present Value Calculation: n ) i 1 ( 1 PVIF + = Basic Case A PVIF = 1 ÷ (1 + 0.02) 4 = 0.9238 B PVIF = 1 ÷ (1 + 0.10) 2 = 0.8264 C PVIF = 1 ÷ (1 + 0.05) 3 = 0.8638 D PVIF = 1 ÷ (1 + 0.13) 2 = 0.7831 P4-12. LG 2: Present Value Concept: PV n = FV n × (PVIF i%,n )
Chapter 4 Time Value of Money 75 Intermediate (a) PV = FV 6 × (PVIF 12%,6 ) (b) PV = FV 6 × (PVIF 12%,6 ) PV = \$6,000 × (.507) PV = \$6,000 × (0.507) PV = \$3,042.00 PV = \$3,042.00 Calculator solution: \$3,039.79 Calculator solution: \$3,039.79 (c) PV = FV 6 × (PVIF 12%,6 ) PV = \$6,000 × (0.507) PV = \$3,042.00 Calculator solution: \$3,039.79 (d) The answer to all three parts are the same. In each case the same questions is being asked but in a different way. P4-14. LG 2: Time Value: PV = FV n × (PVIF i%,n ) Intermediate PV = \$100 × (PVIF 8%,6 ) PV = \$100 × (0.630) PV = \$63.00 Calculator solution: \$63.02 P4-16. LG 2: Time Value Comparisons of Lump Sums: PV = FV n × (PVIF i%,n ) Intermediate ( a) A PV = \$28,500 × (PVIF 11%,3 ) B PV = \$54,000 × (PVIF 11%,9 ) PV = \$28,500 × (0.731) PV = \$54,000 × (0.391) PV = \$20,833.50 PV = \$21,114.00 Calculator solution: \$20,838.95 Calculator solution: \$21,109.94 C PV = \$160,000 × (PVIF 11%,20 ) PV = \$160,000 × (0.124) PV = \$19,840.00 Calculator solution: \$19,845.43 (b) Alternatives A and B are both worth greater than \$20,000 in term of the present value.

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## This note was uploaded on 09/29/2010 for the course BUSI BUS taught by Professor Gg during the Spring '10 term at CUNY Baruch.

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dachen2007118963_2 - Chapter 4 Time Value of Money E4-2....

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