IOE+201+Homework+1+Solutions

IOE+201+Homework+1+Solutions - ) N = $ 3 ) 1 ( 3000 i + = $...

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1 IOE 201 - Economic Decision Making Homework #1 - Solutions 1. (a) Amount at the end of N years is N i P ) 1 ( + Therefore interest earned in year N +1 is N i iP ) 1 ( + (b) Amount at the end of N +1 years = ( Amount at the end of N years) + (Interest earned in year N +1) = N N i iP i P ) 1 ( ) 1 ( + + + = ) 1 ( ) 1 ( i i P N + + = 1 ) 1 ( + + N i P 2. Simple Interest = iPN = (0.07)($10,000)(20) = $14,000 Compound Interest = F – P = P (1 + i ) N – P = ($10,000){(1.07) 20 – 1} = $28,696.84 3. (a) F = P (1 + i ) N . $6000 = P (1.08) 5 = 1.4693 P . 4693 . 1 6000 $ = P = $4083.58 (b) F = P (1 + i ) N = $15,000(1.08) 4 = $20,407.33 4. Expects to pay simple interest: iPN = (0.16)($10,000)(5) = $8000 Interest due with compounding = F – P = P (1 + i ) N – P = ($10,000){(1.16) 5 – 1} = $11,003.42 5. (a) Amount at the end of 3 years is P (1 + i ) N = $ 3 ) 1 . 0 1 ( 3000 + = $ ) 331 . 1 ( 3000 × = $3993 (b) If earning simple interest, amount at the end of 3 years would be P + iPN = $ { } ) 3 1 . 0 ( 1 3000 × + = $3000 × 1.3 = $3900. Difference = $(3993 - 3900) = $93 (c ) Amount at the end of 3 years is P (1 + i
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Unformatted text preview: ) N = $ 3 ) 1 ( 3000 i + = $ ) 3 3 1 ( 3000 3 2 i i i + + + If earning simple interest, amount at the end of 3 years would be P + iPN = $ ) 3 1 ( 3000 i + . Difference = $ ) 3 1 ( 3000 ) 3 3 1 ( 3000 3 2 i i i i +-+ + + = $ ) 3 ( 3000 3 2 i i + = $ ) 3 ( 3000 2 + i i . 2 6. F = P (1 + i ) N . N P F ) 07 . 1 ( 3 + = = . ) 07 . 1 ln( 3 ln N = . 24 . 16 0677 . 0986 . 1 ) 07 . 1 ln( 3 ln = = = N years. Since interest is compounded only once a year, takes 17 years . 7. P = $200. Interest rate is r per year. Period for compounding interest is ½ year. So interest rate i per period is i = r /2, and number of periods N in 1 year is N = 2. Future worth F after 1 year is $ N i ) 1 ( 200 + = $ 2 2 ) 1 ( 200 r + = $ ) 1 ( 200 4 2 r r + + Interest earned F – P = ${ ) 1 ( 200 4 2 r r + + – 200 } = $ ) ( 200 4 2 r r + = $ ) 4 ( 50 + r r ....
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This note was uploaded on 03/18/2010 for the course IOE 201 taught by Professor Dennisblumenfield during the Fall '09 term at University of Michigan-Dearborn.

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IOE+201+Homework+1+Solutions - ) N = $ 3 ) 1 ( 3000 i + = $...

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