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

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

View Full Document Right Arrow Icon
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 .
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

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

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online