Continuous compounding, Mathematics

Assignment Help:

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


Related Discussions:- Continuous compounding

Brahmaguptas problem, How to solve Brahmaguptas Problem? Explain Brahmagupt...

How to solve Brahmaguptas Problem? Explain Brahmaguptas Problem solving method?

Apply depth-first-search to find out the spanning tree, Apply depth-first-s...

Apply depth-first-search to find out the spanning tree for the subsequent graph with vertex d as the starting vertex.        Ans: Let us begin with node'd'. Mark d as vi

Ratio, the ratio of dogs to cats is 2 to 9.if there are 10 dogs how many ca...

the ratio of dogs to cats is 2 to 9.if there are 10 dogs how many cats are there?

Using a number strip substract , Another aid that can help children pract...

Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means

Trignometry, Define the given satatement : 1.sin90-sin89=sin10 using pythag...

Define the given satatement : 1.sin90-sin89=sin10 using pythagoras theoram 2. How can any value of sin and cosis always given any value of cosec.

Find the frame of a quadratic polynomial , If α, β are the zeros of the pol...

If α, β are the zeros of the polynomial x 2 +8x +6 frame a Quadratic polynomial whose zeros are a)  1/α and  1/β b) 1+ β/α , 1+ α/β. Ans. P(x) = x 2 +8x +6 α + β = -8

Index shift - sequences and series, Index Shift - Sequences and Series ...

Index Shift - Sequences and Series The main idea behind index shifts is to start a series at a dissimilar value for whatever the reason (and yes, there are legitimate reasons

The definition of the limit, The Definition of the Limit In this secti...

The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits

How many types of integer operatiions explain, How many types of Integer Op...

How many types of Integer Operatiions explain? Adding Integers The rules for adding integers are: 1. A positive number plus a positive number equals the sum of the two pos

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd