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# hw2 - Haoyang Huang PID:715099441 BUSI 408 TR 12:30 HW4 1...

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Haoyang Huang PID:715099441 BUSI 408 TR 12:30 HW4 1. The future value increases and the present value decreases. 3. The better deal is the first option (equal installments) since the present value of the increasing amount is lower for the second option. 5. Freshmen. Because the freshman can use the money for much longer before interest starts to accrue. 1. Simple interest rate: r=\$5,000 × .09 = \$450 Interest=\$450 × 10 = \$4,500 in interest. The total balance will be \$5,000 + 4,500 = \$9,500 Compound: FV = PV(1 + r ) t FV = \$5,000(1.09) 10 = \$11,836.82 The difference is: \$11,836.82 – 9,500 = \$2,336.82 2. FV = PV(1 + r ) t a. FV = \$1,000(1.06) 10 = \$1,790.85 b. FV = \$1,000(1.09) 10 = \$2,367.36 c. FV = \$1,000(1.06) 20 = \$3,207.14 d. The interest compounds on the interest already earned in the past period. Your future values grow exponentially in compound interest. 3. FV = PV(1 + r ) t PV = \$15,451 / (1.07) 6 = \$10,295.65 PV = \$51,557 / (1.15) 9 = \$14,655.72 PV = \$886,073 / (1.11) 18 = \$135,411.60 PV = \$550,164 / (1.18) 23 = \$12,223.79 15. EAR = [1 + (APR / m )] m – 1 EAR = [1 + (.08 / 4)] 4 – 1 = 8.24% EAR = [1 + (.18 / 12)] 12 – 1 = 19.56% EAR = [1 + (.12 / 365)] 365 – 1 = 12.75% EAR = e q – 1 EAR = e .14 – 1 = .1503 or 15.03% 16. EAR = [1 + (APR / m )] m – 1 EAR = .1030 = [1 + (APR / 2)] 2 – 1 APR = 10.05% EAR = .0940 = [1 + (APR / 12)] 12 – 1 APR = 9.02%

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EAR = .0720 = [1 + (APR / 52)] 52 – 1 APR = 6.96% EAR = e q – 1 APR = ln(1 + EAR) APR = ln(1 + .1590) APR = 14.76% 21. FV = PV(1 + r ) t a. FV = \$1,000(1.08) 7 = \$1,713.82 b. FV = \$1,000(1 + .08/2) 14 = \$1,731.68 c. FV = \$1,000(1 + .08/12) 84 = \$1,747.42 d. FV = PV e Rt FV = \$1,000 e .08(7) = \$1,750.67 e. Because interest is earned on interest earned in the past period. The shorter the compounding period, the more interest to be compounded, and the greater the
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