Ch.9_Solution_Manual_Ed.1_v4_

Ch.9_Solution_Manual_Ed.1_v4_ - Exercises 9.1 Calculate the...

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Exercises 9.1 Calculate the missing values for Problems 1 and 2 Exercise 9.1, Solution 1: Nominal Interest Rate, Compounding Frequency, and Time Period Number of compounding periods per year ( m ) Periodic Interest Rate ( i ) Terms in Years (t) Number of Compounding Periods for the Term (n) a. 5% compounded semi- annually for 2 years 2 2.5% 2 years 4 b. 11.4% compounded quarterly for 1 year and 6 months 4 2.85% 1 year and 6 months 6 c. 8.4% compounded monthly for 1 year and 7 months 12 0.70% 1 year and 7 months 19 d. 7.3% compounded daily for 120 days 365 0.02% 120 a. j = 5% = 0.05, m = 2 = 0.025 = 2.5% t = 2 years = 4 b. j = 11.4% = 0.114, m = 4 = 0.0285 = 2.85% t = 1 year and 6 months = 6 c. i = 0.7% = 0.007, m = 12 j = i × m = 0.007 × 12 = 0.084 = 8.4% compounded monthly t = 1 year and 7 months = 19 d. i = 0.02% = 0.0002, m = 365 j = i × m = 0.0002 × 365 = 0.073 = 7.3% compounded daily t = 120 days = years = 120 Exercise 9.1, Solution 3: i = 2.2% = 0.022, m = 12, j = i × m = 0.022 × 12 = 0.264 = 26.4% compounded monthly Therefore the nominal interest rate is 26.4% compounded monthly. Exercise 9.1, Solution 5: j = 4.28% = 0.0428, i = 2.14% = 0.0214, i = j / m , = 2
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Therefore, the compounding frequency is semi-annually. Exercise 9.1, Solution 7: t = 6 years, m = 2, n = m × t = 2 × 6 = 12 Therefore, the number of compounding periods is 12. Exercise 9.1, Solution 9: t = 16 years and 6 months = 16 + = 16.5, n = 66, n = m × t m = = = 4 Therefore, the compounding frequency is quarterly. Exercise 9.1, Solution 11: i = 2.25%, j = 4.5% = 2 n = m × t = 2 × 8 = 16 Therefore, there are 16 compounding periods. Exercise 9.1, Solution 13: i = 0.5% = 0.005, n = m × t = 4 j = m × i = 4 × 0.005 = 0.02 = 2% Therefore, the nominal interest rate of the loan is 2%. 2
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Exercises 9.2 Calculate the missing values for Problems 1 and 2: Exercise 9.2, Solution 1: Present Value ( PV ) Nominal Interest Rate ( j ) Compounding Frequency ( m ) Time Period ( t ) Periodic Interest Rate ( i ) Number of Compounding Periods ( n ) Future Value ( FV ) a. $1000.00 5.11% 2 5 years and 6 months 2.555% 11 $1319.85 b. $3550.50 4.65% 4 2 years and 3 months 1.1625% 9 $3939.72 c. $16,500.0 0 6.30% 12 219 days 0.525% 7.2 $17,133.94 d. $9650.75 6.57% 1 11 years and 3 months 6.57% 11.25 $19,744.88 a. PV = $1000, t = 5 years and 6 months = 5.5 years, j = 5.11% = 0.0511, m = 2, = 0.02555 = 2.555% n = m × t = 2 × 5.5 = 11 FV = PV (1 + i ) n = 1000 (1 + 0.02555) 11 = 1319.851981. .. = $1319.85 N I/Y P/Y C/Y PV PMT FV 11 5.11 2 2 –1000 0 ? FV (calculator) = 1319.851981 b. PV = $3550.50, t = 2 years and 3 months = 2 + = 2.25 years, i = 1.1625% = 0.011625, m = 4 j = i × m = 0.011625 × 4 = 0.0465 = 4.65% n = m × t = 4 × 2.25 = 9 FV = PV (1 + i ) n = 3550.50 (1 + 0.011625) 9 = 3939.721274. .. = $3939.72 N I/Y P/Y C/Y PV PMT FV 9 4.65 4 4 –3550.50 0 ? FV
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Ch.9_Solution_Manual_Ed.1_v4_ - Exercises 9.1 Calculate the...

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