Continuous compounding, Mathematics

If r per annum is the rate at which the principal A is compounded annually, then at the end of k years, the money due is

         Q = A (1 + r)k

Suppose compounding is done continuously. i.e. at every instant the principal A is compounded at R per annum. Then,

         Q = A eRk

The relationship between R and r is given by the following reasoning:

         A (1 + r)k = A eRk

This implies,      
(1 + r)k = (eR)k  
1 + r = eR  
r = eR - 1  
R = ln (1 + r)  

Example 

If R   = 5.25%, then ln(1 + r) = 5.25% or r = 5.39%

Example 

Suppose Rs.100 is being compounded annually at the rate of 10% per annum. What is the future value of Rs.100 at the end of the third year? What is the effective continuously compounded rate of interest? What is the future value of Rs.100 at the end of the third year, using this interest rate?

FV(Rs.100) = 100 x (1.10)3  = 133.1

If r = 0.1, then the continuously compounded rate of interest R is given by

R = ln(1 + 0.1) = 0.0953

FV(Rs.100) = 100 e0.0953 x 3 = 100 x 1.331 = 133.1

Posted Date: 9/13/2012 6:04:38 AM | Location : United States







Related Discussions:- Continuous compounding, Assignment Help, Ask Question on Continuous compounding, Get Answer, Expert's Help, Continuous compounding Discussions

Write discussion on Continuous compounding
Your posts are moderated
Related Questions
if a&b are aconsra

Show that the first-order integrated rate expression can be written as [A] t = [A] 0 e -n(in)t where n represents the number of elapsed halftimes. Sketch the plot of [A] 1

how do you make a tnslation

howmany numbers made by digit 0,1,2,3,5,7,9 but any digit isnot repeted

CONSTRUCTING TABLES VERSUS ROTE LEARNING :  Ask any adult how she would help a child to acquire simple multiplication facts. There is a very strong possibility that she would say,



Differentiate following functions. (a) f ( x ) = 15x 100 - 3x 12 + 5x - 46 (b) h ( x ) = x π   - x √2  Solution (a)    f ( x ) = 15x 100 - 3x 12 + 5x - 46 I

prove that cos(a)/1-sin(a)=tan(45+A/2)

what is the domain of the function f(x)= 2x^2/x^2-9