My Math Forum  

Go Back   My Math Forum > Science Forums > Economics

Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance


Reply
 
LinkBack Thread Tools Display Modes
February 5th, 2008, 07:10 AM   #1
Member
 
Joined: Sep 2007

Posts: 30
Thanks: 0

Solving for exponential rate of return

I wish to calculate the rate of return for an investment account with periodic investments. I would also like the rate of return to be the exponential rate so that number of times compounded is infinite.

So an account balance=B after time=T at a rate=R will be worth B*exp(T*R).

Suppose for a time period of one year there are 2 deposits (D1, D2) into an account with starting balance B. At the end of the year B has been invested for 1 year, D1 has been invested for T1 of the year and D2 has been invested for T2 of the year. The equation for the balance at the end of the year for rate=R is:

B*exp(R)+D1*exp(T1*R)+D2*exp(T2*R)

If I know my account balance is K at the end of the year how do I solve the equation :

K=B*exp(R)+D1*exp(T1*R)+D2*exp(T2*R) for R

I currently use the solver program in excel but I would assume there is some financial equation that would solve for R.
RFurball is offline  
 
February 5th, 2008, 07:42 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
There's no obvious solution -- likely no closed form solution exists, depending on your choice of T1 and T2. You can see this by letting E = exp(R). Then

K = B*E + D1*E^T1 + D2*E^T2

and so you have a fractional power equation.

I'd use a generic solver like bisection, Newton's method, or the secant method.
CRGreathouse is offline  
February 21st, 2008, 06:02 PM   #3
STV
Member
 
Joined: Aug 2007

Posts: 93
Thanks: 0

Re: Solving for exponential rate of return

Quote:
Originally Posted by RFurball
I wish to calculate the rate of return for an investment account with periodic investments. I would also like the rate of return to be the exponential rate so that number of times compounded is infinite.

So an account balance=B after time=T at a rate=R will be worth B*exp(T*R).

Suppose for a time period of one year there are 2 deposits (D1, D2) into an account with starting balance B. At the end of the year B has been invested for 1 year, D1 has been invested for T1 of the year and D2 has been invested for T2 of the year. The equation for the balance at the end of the year for rate=R is:

B*exp(R)+D1*exp(T1*R)+D2*exp(T2*R)

If I know my account balance is K at the end of the year how do I solve the equation :

K=B*exp(R)+D1*exp(T1*R)+D2*exp(T2*R) for R

I currently use the solver program in excel but I would assume there is some financial equation that would solve for R.
What you are calculating is the continuous internal rate of return (IRR). There is no closed form, but there is an Excel IRR function that iterates attempted solutions until it finds one. The function returns the annualized one year return so you would have to convert it to continous by ln(1+IRR)
STV is offline  
Reply

  My Math Forum > Science Forums > Economics

Tags
exponential, rate, return, solving



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
internal rate of return specific for this exercise lauretta Economics 1 October 2nd, 2012 01:29 PM
Exponential growth rate? Campus Algebra 1 April 11th, 2012 10:42 AM
exponential problem solving dmxnemesis Calculus 3 October 26th, 2010 11:07 PM
need help to find interest rate of return by excel nastenka Economics 0 December 24th, 2009 01:12 PM
solving for exponential value jamesuminator Algebra 4 December 14th, 2008 07:24 AM





Copyright © 2019 My Math Forum. All rights reserved.