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what number is for hourly compound interest

 Apr 21, 2014

Best Answer 

 #1
avatar+129918 
+5

Re: what number is for hourly compound interest

I'm not aware that interest is usually compounded per hour, but we might "devise" a formula to do so.

The normal "formula" is just this

A(t) = A_0 \left(1 + \frac {r} {n}\right) ^ {\lfloor nt \rfloor}

Where

A(t)  = the total amount accumulated after some period at some rate of interest

A0 = the orginal investment or principal

r = annual rate of interest (expressed as a decimal ....   5% = .05, for example)

n = number of compoundings per year

t = time (in years)

The number of compoundings per year = 24 hours in a day x 365 days = 8760... (Note that your mileage may vary here if we have to account for a "leap" year !!!)

To find out how much interest is earned over some time period, just subtract A0  from A(t) at the end of the period.

It might seem that hourly compounding would generate WAY more interest in a year than some other method, say, quarterly compounding, but it isn't so. For instance, 5% interest on $1000 compunded hourly for one year results in only about 33 cents more interest than the same amount at the same interest rate compounded quarterly.

Hope that helps

P.S. - There may be other forum members who are are far better versed in finance than I am. Perhaps some of them might contribute some other "formula" - if they know of one !!!

 Apr 21, 2014
 #1
avatar+129918 
+5
Best Answer

Re: what number is for hourly compound interest

I'm not aware that interest is usually compounded per hour, but we might "devise" a formula to do so.

The normal "formula" is just this

A(t) = A_0 \left(1 + \frac {r} {n}\right) ^ {\lfloor nt \rfloor}

Where

A(t)  = the total amount accumulated after some period at some rate of interest

A0 = the orginal investment or principal

r = annual rate of interest (expressed as a decimal ....   5% = .05, for example)

n = number of compoundings per year

t = time (in years)

The number of compoundings per year = 24 hours in a day x 365 days = 8760... (Note that your mileage may vary here if we have to account for a "leap" year !!!)

To find out how much interest is earned over some time period, just subtract A0  from A(t) at the end of the period.

It might seem that hourly compounding would generate WAY more interest in a year than some other method, say, quarterly compounding, but it isn't so. For instance, 5% interest on $1000 compunded hourly for one year results in only about 33 cents more interest than the same amount at the same interest rate compounded quarterly.

Hope that helps

P.S. - There may be other forum members who are are far better versed in finance than I am. Perhaps some of them might contribute some other "formula" - if they know of one !!!

CPhill Apr 21, 2014
 #2
avatar+118687 
0

Hi Chris,

Did you learn that latex already? I am impressed!

 Apr 22, 2014
 #3
avatar+129918 
0

Unfortunately not......I copied the formula straight from Wikipedia (I actually knew it....but I'm too lazy to type !! LOL!!)

I found a LaTex "primer" on the Internet that I'm trying to work through, but it contains a lot of technical mumbo-jumbo that is indecipherable (particularly about saving/displaying output).  I learned this much, at least....."LaTex" isn't pronounced as it seems !!!

I think I'm going to watch the video(s) that you suggested.....I'm sure they're clearer

 

P.S. - I know we're not supposed to be passing messages back and forth in the forum, but I don't fully trust the "message" service, yet!!!

 Apr 22, 2014

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