# How NOT to calculate daily compound interest rate

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I wanted to work out how much interest I would gain by leaving some money in a certain account for a few days. I knew I could derive this myself using logarithms but I was too lazy, so I searched google and clicked on the top result which turned out to be completely incorrect.

The author David Ingram recommends calculating a weekly interest rate from an annual interest rate by dividing by 12 months then 4 weeks per month which is just plain stupid, as the correct answer might be to divide by 365 (or 366!) days, then multiply by 7 days per week.

David Ingram fails to consider this distinction again and compounds his error when he suggests calculating your daily interest rate simply by dividing the incorrect weekly rate by 7. His method of calculation causes an error of 8% which is pretty significant!

This is of course assuming that we are talking about simple rather than compound interest, although the author makes no mention of this distinction. Certainly in the UK its rare to see simple interest used in financial products.

So if we're actually interested in the compound daily interest rate that is equivalent to a particular annual interest rate, this is what we need:

$Daily Interest Rate = e^ {log (Annual Interest Rate) / 365}$

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### 2 Responses to How NOT to calculate daily compound interest rate

1. Richard says:

Confusing. Let AnnualInterestRate = 6.25%, exp(log(6.25)/365) = 1.005033% which is clearly incorrect. It isn't correct if you do 0.0625 either.

From what I can tell, the correct formula is:

DailyInterestRate = ((1+(AnnualInterestRate/100)) ^ (1/365.0) - 1) * 100

Where the AnnualInterestRate = 6.25 for example for 6.25%, which gives a rate of 0.0166%

If you take 55,000 + 55,000 * (6.25 / 100) you get 58,437. This is an annual rate of 6.25%. If you then take 55,000 and apply compounding interest of 0.0166% 365 times, you also get 58,437.

I suspect you have the right formula in there somewhere, but since your post is fairly high on google now it made sense to post my findings.

• frankster says:

The main difference between our formulas is simply that I have been expressing an interest rate in a slightly different form to yours (e.g. 6.25% as 1.0625). Your formula handles the conversion between percentage and multiplier which makes it a bit more involved - but perhaps more useful.

I've obviously not been anywhere near clear enough about what's going on here so I will update the post in due course. As this article was intended to clarify some incorrect information on the internet, its super important that I don't go on to confuse others!

Thank you for taking the time to respond.