IOE+201+Notes+3

# IOE+201+Notes+3 - Economic Equivalence 7 annual interest...

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1 Economic Equivalence 7% annual interest rate: IOE 201 Lecture Notes 3 Years 0 1 2 3 4 5 \$2000 \$2000(1+0.07) 3 \$2450 Years 0 1 2 3 4 5 \$2805(1+0.07) - 2 \$2450 \$2805

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2 Economic Equivalence 0 1 2 3 4 5 \$50 \$40 \$70 \$80 \$100 \$50 0 1 2 3 4 5 = Lump Sum = ? What is the equivalent lump-sum amount in period 3 at 5% annual interest rate? Interest Periods Interest Periods
3 0 1 2 3 4 5 \$50 \$40 \$70 \$80 \$100 \$50 Interest Periods \$ 50(1+0.05) 3 + 70(1+0.05) 2 + 40(1+0.05) 2 + 80 + 50(1+0.05) - 1 + 100(1+0.05) - 2 = \$395.38 Economic Equivalence

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4 Equivalence of Loan Payment Schedules P = \$10,000 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 A A A A A A A F 0 1 2 3 4 5 6 7 8 \$1000 \$10,000 Total Amount Paid A Single payment : Equal payments A = \$1874: Interest payments + Principal : \$ 21,436 \$ 14,992 \$ 18,000 8-year, \$10,000 loan, interest rate 10% per year, compounded annually P = \$10,000 P = \$10,000 Wide differences in total amount paid, but all 3 payment schedules are equivalent
5 0 1 2 3 4 5 6 7 8 P G 2 G 3 G 4 G 5 G 6 G Linear Gradient Series of Payments 7 G Present worth P = 8 4 3 2 ) 1 ( 7 ) 1 ( 3 ) 1 ( 2 ) 1 ( 0 i G i G i G i G + + + + + + + + + Interest Periods Interest rate i per period Gradient amount G

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6 Linear Gradient Series of Payments:
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## This note was uploaded on 03/17/2010 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+Notes+3 - Economic Equivalence 7 annual interest...

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