# Thread: Compounding Interest (daily) (2000)

1. ## Compounding Interest (daily) (2000)

So I've been doing some research, but I don't know exactly how all of these financial options work. Right now I'm trying to create a formula in Excel to calculate the amount of return on a \$2500 initial deposit into an account with 2% daily compounding interest (paid monthly)....anyone know any sites to shed some light/any formulas in excel that I could use? Thanks <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

2. ## Re: Compounding Interest (daily) (2000)

See the links provided in the thread starting at <post#=511,840>post 511,840</post: >.

3. ## Re: Compounding Interest (daily) (2000)

See the attached file.

<font color=red>note that you must have the "Analysis Toolpak" installed, since this worksheet uses the "EOMonth" formula available in the toolpak</font color=red>

As you know, the more often interest is compounded, the faster the balance grows - the interest in a year will be
<pre>i = P * ((1 + r/n)^n - 1)</pre>

where P is the initial principal, r is the stated (or nominal) annual rate, and n is the number of compounding periods. There is a limit though - as n gets larger and larger, the interest in the year get closer and closer to the "continuously compounded" interest or,
<pre> i = P * (exp(r * frac) - 1) </pre>

where "frac" is the fraction of the year we are talking about. If we are looking at a whole year then i = P x (exp® - 1) when interest is compounded continuously. If we are looking at a part of a year, then frac = the number of days the balance is outstanding divided by 365 (the difference between daily and continuous compounding is not even close to material).

The attached sheet determines the number of days in each month that the principal has been on deposit, and then uses the continuous compounding function to calculate the accrued interet to the next month end. The interest is added to the principal - but you don't need to do that; you could, for example, just calculate the interest over the three year life as
<pre> i = P * (exp(r * 3) - 1) </pre>

<pre> i = 2500 * (exp(0.02 * 3) - 1) = 154.59 </pre>

4. ## Re: Compounding Interest (daily) (2000)

Dean (and Hans) thank you both very much, for all the information. Your spreadsheet does exactly what I wondered about.

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