# H3 - Continuous Compounding Some Basics W.L Silber Because...

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Continuous Compounding: Some Basics W.L. Silber Because you may encounter continuously compounded growth rates elsewhere, and because you will encounter continuously compounded discount rates when we examine the Black-Scholes option pricing formula, here is a brief introduction to what happens when something grows at r percent per annum, compounded continuously. We know that as n (1) L 71828183 . 2 1 1 = = + e n n In our context, this means that if \$1 is invested at 100% interest, continuously compounded, for one year, it produces \$2.71828 at the end of the year. It is also true that if the interest rate is r percent, then \$1 produces r e dollars after 1 year. For example, if 06 . = r we have 0618365 . 1 1 \$ 06 . = e After two years, we would have: 127497 . 1 ) 2 ( 06 . 06 . 06 . = = e e e More generally, investing P at r percent, continuously compounded, over t years, produces (grows to) the amount F according to the following formula: (2) F Pe rt = For example, \$100 invested at 6 percent, continuously compounded, for 5 years produces 98588 . 134 \$ 100 \$ ) 5 ( 06 .

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## This note was uploaded on 02/04/2010 for the course ECON 106v taught by Professor Miyakawa during the Spring '08 term at UCLA.

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H3 - Continuous Compounding Some Basics W.L Silber Because...

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