IOE+201+Midterm+Solutions

IOE+201+Midterm+Solutions - IOE 201 - Economic Decision...

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1 IOE 201 - Economic Decision Making Fall 09 Midterm Exam - Solutions 1. (a) With quarterly compounding, effective annual interest rate = 1 4 1 4 - + r = 1 4 12 . 0 1 4 - + = ( ) 1 03 . 1 4 - = 0.1255 = 12.55% (b) With continuous compounding, effective annual interest rate = 1 - r e For same effective interest rate as in (a), 1 - r e = 0.1255 . r e = 1 + 0.1255 . Nominal annual interest rate r = ln(1 + 0.1255) = 0.1182 = 11.82% 2. (a) Number of interest periods per year M = 4. Interest rate per interest period, i = r / M = r /4. Number of interest periods C in ½ a year = M /2 = 2. Amount paid back = $ C i ) 1 ( 400 , 2 + = $ 2 4 ) 1 ( 400 , 2 r + = $ ) 1 ( 400 , 2 4 2 2 r r + + Interest paid = ) 1 ( 400 , 2 $ 16 2 2 r r + + – $2,400 = $ ) ( 400 , 2 16 2 2 r r + = $150 r ( r + 8) Or, effective interest rate in ½ a year = 1 ) 1 ( - + C M r = 1 ) 1 ( 2 4 - + r = ) ( 16 2 2 r r + . Interest paid = $ ) ( 400 , 2 16 2 2 r r + = $150 r ( r + 8) (b) With continuous compounding, amount paid back = $ 2 400 , 2 r e . Interest paid = $ 2 400 , 2 r e – $2,400 = $ ) 1 ( 400 , 2 2 - r e Or, effective interest rate in ½ a year = 1 2 - r e . Interest paid = $ ) 1 ( 400 , 2 2 - r e If r = 10% = 0.1: Interest paid with continuous compounding = $ ) 1 ( 400 , 2 2 1 . 0 - e = $123.05 Interest paid with quarterly compounding = $150(0.01)(0.01 + 8) = $121.50 Extra interest paid with continuous compounding = $123.05 - $121.50 = $1.55 3. (a) Cash flow diagram: years 0 1 2 3 $4000 4 5 6 7 $4000 $5000 $5000 $5000 $5000 $6000 ? Let
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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+Midterm+Solutions - IOE 201 - Economic Decision...

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