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

Steps for radio test - sequences and series, Steps for Radio test Assum...

Steps for Radio test Assume we have the series ∑a n Define, Then, a. If L b. If L>1 the series is divergent. c. If L = 1 the series might be divergent, this i

Define the correlations, A retention counselor at a state university believ...

A retention counselor at a state university believes that freshman year success is related to high school standard tests in math and reading, and in the number of credits the stude

Explain basic concepts of parallel lines, Explain Basic Concepts of Paralle...

Explain Basic Concepts of Parallel Lines ? Parallel lines are defined in section 1.2 and we use "//" to denote it. From the definition, we can get the following two consequenc

Evaluate the perimeter of the plot of land, Evaluate the perimeter of the p...

Evaluate the perimeter of the plot of land. a. 260 m b. 340 m c. 360 m d. 320 m To evaluate the perimeter, we must know the length of all sides. According to the dia

Composite functions, f(x)=4x-3 and g(x)=(x+3)/4 a)Find the function fg(x) ...

f(x)=4x-3 and g(x)=(x+3)/4 a)Find the function fg(x) b)Hence describe the relationship between the functions f and g c)Write down the exact value of fg(sqrt(3))

Diffrential integral , All the integrals below are understood in the sense ...

All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]

Solve for x and y liner equation, Solve for x , y (x + y - 8)/2   ...

Solve for x , y (x + y - 8)/2   =( x + 2  y - 14)/3 = (3 x + y - 12 )/ 11   (Ans: x=2, y=6) Ans :     x+ y - 8/2  =   x + 2y - 14 /3  =    3x+ y- 12/11

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