# Ch4 - FIN 301 Homework Solution Ch4 Chapter 4 Time Value of...

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1 FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. €10,000/(1.10) 10 = €3,855.43 b. €10,000/(1.10) 20 = €1,486.44 c. €10,000/(1.05) 10 = €6,139.13 d. €10,000/(1.05) 20 = €3,768.89 2. a. \$100 × (1.10) 10 = \$259.37 b. \$100 × (1.10) 20 = \$672.75 c. \$100 × (1.05) 10 = \$162.89 d. \$100 × (1.05) 20 = \$265.33 5. Present Value Years Future Value Interest Rate a. \$400 11 \$684 % 00 . 5 1 400 684 ) 11 / 1 ( = b. \$183 4 \$249 % 00 . 8 1 183 249 ) 4 / 1 ( = c. \$300 7 \$300 % 0 1 300 300 ) 7 / 1 ( = To find the interest rate, we rearrange the basic future value equation as follows: FV = PV × (1 + r) t r = 1 PV FV ) t / 1 (

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2 7. PV = (2,000 pesos/1.06) + (4,000 pesos/1.06 2 ) + (5,000 pesos/1.06 3 ) = 1,886.79 pesos + 3,559.99 pesos + 4,198.10 pesos = 9,644.88 pesos 8. You should compare the present values of the two annuities; select the annuity with the greater present value. a. 73 . 721 , 7 \$ (1.05) 0.05 1 0.05 1 \$1,000 PV 10 = × × = 73 . 303 , 8 \$ (1.05) 0.05 1 0.05 1 \$800 PV 15 = × × = b. 47 . 192 , 4 \$ (1.20) 0.20 1 0.20 1 \$1,000 PV 10 = × × = 38 . 740 , 3 \$ (1.20) 0.20 1 0.20 1 \$800 PV 15 = × × = When the interest rate is low, as in part (a), the longer (i.e., 15-year) but smaller annuity is more valuable because the impact of discounting on the present value of future payments is less significant. 9. \$100 × (1 + r) 3 = \$115.76 r = 5.00% \$200 × (1 + r) 4 = \$262.16 r = 7.00% \$100 × (1 + r) 5 = \$110.41 r = 2.00% 10. In these problems, you can either solve the equation provided directly, or you can use your financial calculator, setting: PV = ( )400, FV = 1000, PMT = 0, i as specified by the problem. Then compute n on the calculator. a. \$400 × (1.04) t = \$1,000 t = 23.36 periods b. \$400 × (1.08) t = \$1,000 t = 11.91 periods c. \$400 × (1.16) t = \$1,000 t = 6.17 periods
3 11. APR Compounding period Effective annual rate a. 12% 1 month (m = 12/yr) 1.01 12 1 = 0.1268 = 12.68% b. 8% 3 months (m = 4/yr) 1.02 4 1 = 0.0824 = 8.24% c. 10% 6 months (m = 2/yr) 1.05 2 1 = 0.1025 = 10.25% 12. Effectiv e Rate Compounding period Per period rate APR a. 10.00% 1 month (m = 12/yr) 1.10 (1/ 12) 1 = 0.0080 0.096 = 9.6% b. 6.09% 6 months (m = 2/yr) 1.0609 (1/ 2) 1 = 0.0300 0.060 = 6.0% c. 8.24% 3 months (m = 4/yr) 1.0824 (1/ 4) 1 = 0.0200 0.080 = 8.0% 14. APR = 1% × 52 = 52% EAR = (1.01) 52 1 = 0.6777 = 67.77%

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## This note was uploaded on 09/29/2010 for the course FIN 301 taught by Professor Gg during the Spring '10 term at CUNY Baruch.

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Ch4 - FIN 301 Homework Solution Ch4 Chapter 4 Time Value of...

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