IOE+201+Midterm+Solutions

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online