02 Fin 301 Time value mechanics Ulearn

# 02 Fin 301 Time value mechanics Ulearn - Time Value...

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Time Value Mechanics

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2 Investing for a Single Period § r  ”  interest rate (nominal) § P 0 ”  \$ to be invested today § P 1 ”  \$ available next period from  investment ) 1 ( ) 1 ( 1 0 0 0 0 1 r P P r P r P P P + = + = + =
3 Investing for Multiple Periods § Calculating   Future Value: § Discounting: t t t t t r P P r P r P P r P r P P r P r P P r P P ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( 0 0 1 3 0 2 3 2 0 1 2 0 1 + = + = + = + = + = + = + = + = -

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4 Compound Interest § Interest on interest earned in earlier periods ( 29 r r P r P r P P r r P r P r P P + + + = + + + = + = 0 0 0 0 0 0 2 0 2 ) 1 ( ) 1 ( ) 1 ( 0 0 0 0 0 0 1 2 2 P r P r P r P P r P P P + = + + = + = Compound Interest Simple Interest C o m p a r e ! Interest earned on  P0  in period 1 Interest earned on  P0    in period 2 Interest on  interest
5 Interest on Interest ( 29 ( 29 ( 29 ( 29 4 0 3 0 2 0 0 0 4 3 0 2 0 0 0 3 2 0 0 0 2 0 0 1 4 6 4 3 3 2 1 r P r P r P r P P P r P r P r P P P r P r P P P r P P P + + + + = + + + = + + = + = Compound Interest ( 29 r P t P P t × + = 0 0 Simple Interest Ignored with simple Interest The Difference: ( 29 r P t P r P t × - - + × = 0 0 0 ) 1 ( interest   on Interest

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6 Example 3 . 469 , 1 \$ 4693 . 1 000 , 1 ) 08 . 1 ( 000 , 1 ) 1 ( 5 5 0 5 = = = + = r P P 400 , 1 \$ 400 \$ 000 , 1 \$ 5 08 . 0 000 , 1 \$ 000 , 1 \$ 0 0 5 = + = + = + = t r P P P
7 \$0 \$500 \$1,000 \$1,500 \$2,000 \$2,500 \$3,000 \$3,500 0 5 10 15 20 25 Years Value of \$100 @15% Compound vs. Simple Interest

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8 Question 3
9 Question 4

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10 Multiple Cash Flows t C t at time occuring flow cash { } time   in point    at    stream   flow   cash   of   value represent    will   t C P t t 1 2 3 0 C 1 C 2 C 3
Value of Cash Flow at time t > 0 § If r = 10% then the present value (t = 0) is: § Value at t = 2: 1 2 3 0 C 3 =  \$1,000 31 . 751 \$ ) 10 . 1 ( 000 , 1 \$ ) 1 ( 3 3 3 0 = = + = r C P 09 . 909 \$ 10

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## This note was uploaded on 11/01/2011 for the course BUSINESS FIN301 taught by Professor Andrew during the Fall '10 term at University of Alberta.

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02 Fin 301 Time value mechanics Ulearn - Time Value...

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