LN4-InterestRates_Slides

# LN4-InterestRates_Slides - discount rate is r = 0 05 is PV...

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Interest Rates Toolbox February 7, 2011

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Simple vs. Compounded Interest Rates Compounded: Interest is paid on interest earned. Simple Example: \$1 invested with a quarterly simple rate of r at the end of the year yields: (1 + 4 * r ) If the interest is compounded, one gets: (1 + r ) 4
Frequency of Compounding Let r ( n ) be the annual simple rate where payments are made every n periods, within a given year. To get the effective annual rate we would compute the rate r that satisfies: 1 + r = (1 + r ( n ) /n ) n For the same level of interest rate, the larger n the higher the return.

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Present Value Definition : The present value of some future payment is the amount which, when invested today at a given interest rate would result in the value of the future payment. Example: The present value of \$105 if a year if the

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Unformatted text preview: discount rate is r = 0 . 05 is: PV = \$105 1 . 05 = \$100 ◮ We call the discount factor the ratio: d = 1 1 + r Streams of Income ◮ Sequence of future cash-flows: P , P 1 , P 2 . ◮ Present Value: P (0) = P + P 1 / (1 + r ) + . . . + P m / (1 + r ) m ◮ P ( m ) = P (1 + r ) m + P 1 (1 + r ) m-1 + . . . + P m Forward Rates ◮ Spot Rates: Rates that are quoted (and traded) in the present. ◮ These rates might be quoted for bonds/loans of different maturities ◮ Forward rates relate spot rates of different maturities. ◮ Let the one year spot rate be r 1 and the two year spot rate be r 2 (both in annual terms). Then the forward rate f 1 , 2 is defined as: (1 + r 1 )(1 + r 1 , 2 ) = (1 + r 2 ) 2...
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## This note was uploaded on 11/20/2011 for the course ECON 420 taught by Professor Silous during the Spring '11 term at Emory.

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LN4-InterestRates_Slides - discount rate is r = 0 05 is PV...

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