From: Jonathan Bryce 
Newsgroups: uk.finance
Subject: Re: How to calculate interest rate for an annuity?
Date: Fri, 07 Jan 2005 19:25:47 +0000

Inquisitive wrote:

> If I know that the present value today of £75 per year for three years
> is £171.13, how can I calculate what the three-year rate of interest
> is?
> 
> I know (well, think at least) that the formula for calculating the
> present value of an annuity is
> 
> Present Value = C(1/r - 1/r(1+r)^t)
> 
> where C is the payment, r is the rate of interest and t is the number
> of years.
> 
> I imagine it would be possible to solve this for r using the values I
> have indicated above (i.e. C=75 and t=3), but am unsure how to
> rearrange the expression to make r the subject. I also have a feeling
> that I am probably making this more complicated than it needs to be!

You can cheat and get Excel to answer it for you.  Install the Analysis
Toolpack, and use the following formula:

=RATE(3,-75,171.13)

You get the answer 15.0394%, which is the same as Ronald Raygun's answer, so
it must be right.

Alternatively, if you are using OpenOffice.org, then use the formula

=RATE(3;-75;171.13)

You get the same answer.  No need to install additional toolpacks.