IOE+201+Homework+2+Solutions

IOE+201+Homework+2+Solutions - IOE 201 - Economic Decision...

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1 IOE 201 - Economic Decision Making Homework #2 - Solutions 1. Effective interest rate = 0.1256 = (1+ i ) M - 1 where i = interest rate per period and M = number of periods per year. Interest is compounded quarterly, so period is a quarter and M = 4. (a) (1+ i ) 4 = 1 + 0.1256 1+ i = (1.1256 ) 1/4 Interest rate per quarter, i = 0.0300 = 3% (b) Nominal annual interest rate = M × i = 4 × 3% = 12% 2. (a) Monthly compounding: M = 12. Nominal interest rate r = M×i = 12 × 1.5% = 18% (b) Effective interest rate r eff = (1 + i ) M - 1 = (1 + 0.015) 12 - 1 = 19.56% 3. (a) Future worth F = P (1+ i ) N = $1000(1+ 0.15) N $0 $2,000 $4,000 $6,000 $8,000 $10,000 $12,000 $14,000 $16,000 $18,000 0 2 4 6 8 10 12 14 16 18 20 Future Worth F Years, N (b) Future worth at end of 10 years, F 10 = $1,000(1+ 0.15) 10 = $4,045.56 Future worth at end of 20 years, F 20 = $1,000(1+ 0.15) 20 = $16,366.54 F 20 / F 10 = 4.05 > 4 . 4. 1 2 3 4 5 6 7 8 9 10 0 $1000 $1500 $2000 F Years F = $1,000(1+ 0.08) 10 + $1,500(1+ 0.08) 8 + $2,000(1+ 0.08) 6 = $8,109
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IOE+201+Homework+2+Solutions - IOE 201 - Economic Decision...

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