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

Derivative and differentiation, Derivative and Differentiation The pro...

Derivative and Differentiation The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is de

Counters and registers, design a synchronous, recycling, MOD-12 counter wit...

design a synchronous, recycling, MOD-12 counter with D FF''s. Use the states 0000 through 1011 in the counter.

Example of negative number, Q. Example of negative number? If you take ...

Q. Example of negative number? If you take an elevator 8 stories  down , what would be the opposite of this? The opposite would be that you take the elevator 8 stories  up .

Discrete-time signals as energy or power signals, Classify the following di...

Classify the following discrete-time signals as energy or power signals. If the signal is of energy type, find its energy. Otherwise, find the average power of the signal. X 1

Determine the number of full withdrawals, A worker retires with a lump sum ...

A worker retires with a lump sum superannuation benefit of $500,000. She immediately invests this money in a fund earning 5% pa effective. One year after retirement she begins maki

Complex root - fundamental set of solutions, Example : Back into the comple...

Example : Back into the complex root section we complete the claim that y 1 (t ) = e l t cos(µt)        and      y 2 (t) = e l t sin(µt) Those were a basic set of soluti

., WRITE the condition that should be fulfilled by two matrices A&B to get ...

WRITE the condition that should be fulfilled by two matrices A&B to get the product AB and BA

Objectives to knowing your maths learner, Objectives After studying th...

Objectives After studying this unit, you should be able to briefly describe the developmental stages of children's thinking and learning processes; assess the levels

Explain multiples, Explain Multiples ? When a whole number is multiplie...

Explain Multiples ? When a whole number is multiplied by another whole number, the results you get are multiples of the whole numbers. For example,  To find the first four mult

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