Wikipedia:Reference desk/Archives/Mathematics/2024 April 18

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April 18

How do I calculate the daily interest rate, when given the effective annual interest rate?

Interest compounds daily. The effective annual interest rate is 5.15%. Is there some formula to calculate what is the actual daily interest rate? Using a lot of trial and error on spreadsheets, I estimated that the daily interest rate is 5.02235% (or so). But, that was through a lot of trial and error … and it only comes “close to” an estimate of the actual daily interest rate. Is there some mathematical formula that will give me the exact figure? Thanks. 32.209.69.24 (talk) 02:04, 18 April 2024 (UTC)

To clarify, when I estimated the daily interest rate, I came up with 5.02235% (divided by 365) = 0.01375986301370%. Thanks. 32.209.69.24 (talk) 02:14, 18 April 2024 (UTC)

If I'm interpreting this correctly, then if you are given the annual interest rate $A$, then you want a daily interest rate $D$ such that $(1+{\frac {D}{365}})^{365t}=(1+A)^{t}$, where $t$ is the number of years. Since both sides are exponentials and the only way they can always match is for the bases to match, we can just remove the $t$ to get $(1+{\frac {D}{365}})^{365}=1+A$. Taking the root on each side, you get $1+{\frac {D}{365}}={\sqrt[{365}]{1+A}}$. Rearranging yields $D=365({\sqrt[{365}]{1+A}}-1)$. For your value of $A=0.0515$, this yields $D=0.05022117$, which is close to but slightly off from your value. GalacticShoe (talk) 02:15, 18 April 2024 (UTC)

Thank you so much ... for such a quick reply and for such a detailed explanation. Much appreciated. A follow-up question, if I may. That final formula that you cite contains a "root index" of 365. Is there a comparable formula that can be entered into an Excel spreadsheet? (I have no idea of how to -- or even if -- one can express a root index of 365 in Excel.) Thanks! 32.209.69.24 (talk) 02:29, 18 April 2024 (UTC)

Some preliminary searching indicates that you can just do "value^(1/365)", so for example "365*((1+A)^(1/365)-1)" GalacticShoe (talk) 02:44, 18 April 2024 (UTC)

Thanks a million! Very much appreciated! 32.209.69.24 (talk) 05:21, 18 April 2024 (UTC)

Why is it quintillion...

...and not pentillion? Someone who's wrong on the internet (talk) 05:43, 18 April 2024 (UTC)

All those number names are based on Latin (in this case quinque) rather than Greek (πέντε). --Wrongfilter (talk) 06:14, 18 April 2024 (UTC)

Then why is it pentagon and not quintagon? Someone who's wrong on the internet (talk) 09:07, 18 April 2024 (UTC)

Because -gon is Greek (γωνία = angle, from γόνυ = knee), hence the prefix is Greek, too. Some terms are Greek, others are Latin, mixtures are to be avoided. --Wrongfilter (talk) 09:21, 18 April 2024 (UTC)

German makes a bit more sense when it comes polygons, Dreieck=Triangle, Viereck=Quadrilateral, Fünfeck=Pentagon, ... . Literally (the number in German)+"Eck" = corner or angle. I imagine other languages not so heavily influenced by Latin and Greek are similar, none of this "If it's Tuesday we must be using Greek roots." The word for "polygon" is "Polygon" in German, breaking the pattern, though "Vieleck"="many"+"angle" is used as well. As for the numbers, people still don't seem to agree on what these names even mean (see Long and short scales). When in doubt, use 10¹⁸. --RDBury (talk) 14:21, 18 April 2024 (UTC)

Because there is no master plan covering even all of one discipline's jargon. —Tamfang (talk) 02:49, 1 May 2024 (UTC)

My favourite shape is the octangular quadragon. -- Jack of Oz ^{[pleasantries]} 21:14, 18 April 2024 (UTC)

Like these? —Tamfang (talk) 18:45, 25 April 2024 (UTC)