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

Probability, Mike sells on the average 15 newspapers per week (Monday – Fri...

Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers [7] 2.2 In a given day he will sel

Solid mensuration, what is the importance of solid mensuration?

what is the importance of solid mensuration?

Porportions, how do you solve for porportions?

how do you solve for porportions?

Shares, a person having rs.10 shares of value rs.6000 in a company which pa...

a person having rs.10 shares of value rs.6000 in a company which pays a 7% dividend invested the money gained by selling those shares and bought rs.25 shares at rs.24 per share in

Example of subtraction of fractions, Example of Subtraction of Fractions: ...

Example of Subtraction of Fractions: 1/3 + 1/6 + 1/8 = ____ Using trial & error we could search that 24 is the LCD or smallest number in which 3, 6, and 8 will all divide w

Example of cartesian coordinate graph, Example of Cartesian coordinate Grap...

Example of Cartesian coordinate Graph: Example:   The temperature of water flowing in a high pressure line was measured at regular intervals.  Plot the subsequent recorded da

Properties of radicals, If n is positive integer greater than 1 and a & b b...

If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert

Describe about arithmetic and geometric series, Describe about Arithmetic a...

Describe about Arithmetic and Geometric Series? When the terms of a sequence are added together instead of separated by commas, the sequence becomes a series. You will use seri

Even and odd functions, Even and Odd Functions : This is the final topic ...

Even and Odd Functions : This is the final topic that we have to discuss in this chapter.  Firstly, an even function is any function which satisfies,

Trinomial x2 + 2x + 1 what are the dimensions of the field, A farmer's rect...

A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field? Because the formula for th

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