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

Calculus, how to find the volume

how to find the volume

What is 19% of 26, What is 19% of 26? To ?nd out 19% of 26, multiply 26...

What is 19% of 26? To ?nd out 19% of 26, multiply 26 through the decimal equivalent of 19% (0.19); 26 × 0.19 = 4.94.

Concept, uses of maths concept

uses of maths concept

Number sentences, when i couulate the formula f 64 divided by 65 how do i d...

when i couulate the formula f 64 divided by 65 how do i do this

Show that the vector is in the perfect matching polytope, 1.  Let G = (V,E)...

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =

Compute the derivative, Write an octave program that will take a set of poi...

Write an octave program that will take a set of points {x k , f k } representing a function and compute the derivative at the same points x k using 1. 2-point forward di erence

Determine the minimum cost , A company is taking bids on four construction ...

A company is taking bids on four construction jobs. Three Contractors have placed bids on the jobs. Their bids (in thousands of dollars) are given in the file. (A blank indicates n

Randi takes the stairs at work whenever possible instead, Randi takes the s...

Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa

Marketing research, In pharmaceutical product research doctors visit the pl...

In pharmaceutical product research doctors visit the place to learn what

Geometry, which kind of triangle has no congruent sides ?

which kind of triangle has no congruent sides ?

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