# Thread: Having trouble separating e^in from the equation

1. ## Having trouble separating e^in from the equation

I am working with the formula that calculates the present value annuity factor given that interest is compounded continuously

PVIFA = [1 - e^-in]/[e^i - 1]

I am not able to solve for i or n for the reason that I am not getting the e^in cornered on the left side of the equation

After multiple tries the best I have gotten is

[e^in - 1] / [e^in {e^i-1} ] = PVIFA

Any suggestions on how to proceed for simplifying this further

2. ## Re: Having trouble separating e^in from the equation

Equations of type Ax = B(1 + x)^n cannot be solved directly for x; must be solved numerically.

3. ## Re: Having trouble separating e^in from the equation

Originally Posted by Wilmer
Equations of type Ax = B(1 + x)^n cannot be solved directly for x; must be solved numerically.

Hi Wilmer

After posting the question here I went back with paper and pencil to see what I could do with the equation

And as you stated in your reply, finding i out of this equation was not possible just as it was not possible to find i from the PVIFA equation for discrete compounding of interest PVIFA = [1-(1+i)^-n]/i

However I was able to find n from the equation I posted in my last. For finding interest rate I had to go back to Newton Raphson method to find i out of the equation for PVIFA with continuous compounding of interest. See this link for PVIFA Calculator

Now a question I posted a couple of days ago, may be I was not able to phrase it correctly so let me ask again

As with finding the present value annuity due factor when interest is compounded discretely we simply multiply PVIFA by (1+i) so can I use this same principle when finding present value annuity due factor when interest is compounded continuously by multiplying the PVIFA with e^r to make it as follows

PVIFA = e^r[1 - e^-in]/[e^i - 1]

Does this make sense