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
Testing The Difference Between Two Sample Means (Large Samples) A large sample is defined as one which have 30 or more items as n≥30 whereas n is the sample size In a busine

Explain The Decimal System in detail? A decimal, such as 1.23, is made up of two parts: a whole number and a decimal fraction. In 1.23, the whole number is 1 and the decimal fr

Simplify following and write the answers with only positive exponents.  (a) ( x 8.2 y -0.26 z 2 ) 0.5  (b)  (x 3 y -4.1   / x -2.7 ) -3 Solution  (a) (x 8.2

finding the vertex for the function of the form f(x)=ax^2+bx+c

Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x

WHAT IS PRECALC


I should have an account balance for $50.96. You took out $50.96 for a product on 6/18 which was NOT downloaded or delivered as it not available in the time frame I needed it. I am

The mathematics results of 20 first-year university students are given, together with their results of their performances in the year 12 semester Test and Final Assignment:

A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx