### Author Topic: Compound interest frequency  (Read 632 times)

#### veegsy

• Posts: 10
##### Compound interest frequency
« on: February 15, 2021, 03:10:43 PM »
In my mind when using a compound interest calculator and calculating future growth of my Vanguard mutual index funds, the interest is compounded every day the stock market is open, ie 251 days. But on the calculator below, they say this in the description: "For stock and mutual fund investments, you should usually choose 'Annual'." <-- this is obviously the same as just once per year.

https://www.bankrate.com/calculators/savings/compound-savings-calculator-tool.aspx

Can someone explain this?

#### ctuser1

• Handlebar Stache
• Posts: 1741
##### Re: Compound interest frequency
« Reply #1 on: February 15, 2021, 03:20:03 PM »
If you are calculating for a loan, you need to follow the frequency laid out in the loan paperwork.
e.g.1 - I have had two auto loans - they compounded daily.
e.g.2 - I have dealt with two separate CUs for my mortgage, they compound monthly.

If you are calculating for your own savings rate etc - it's all assumptions and approximations. Generally, for stock market, people like to express returns as CAGR, which is a geometric mean of annual growth over a period of time.

There is no intrinsic harm if you like to use a continuous compounding for this purpose instead of annual CAGR. Indeed, I find the calculations to be far easier and intuitive (natural log and e^x is a lot simpler and intuitive than the ugly looking CAGR formula) with continuous compounding assumptions. If you like daily, all power to you and calculate away. I find daily to be even uglier than annual, but you do it if you like it.

One issue that can happen if you choose non-conventional compounding frequency is that you won't be able to easily compare your numbers against numbers from bankrate - for example, because they will follow a different convention comparing theirs to yours would be apples to oranges. So it is generally more convenient to follow the widely used convention like CAGR when you are dealing with the stock market returns.

« Last Edit: February 15, 2021, 03:26:20 PM by ctuser1 »

#### Telecaster

• Magnum Stache
• Posts: 2945
• Location: Seattle, WA
##### Re: Compound interest frequency
« Reply #2 on: February 15, 2021, 03:26:24 PM »
And the frequency annual vs. daily vs. continuous doesn't really matter a whole lot.

#### MustacheAndaHalf

• Walrus Stache
• Posts: 5306
##### Re: Compound interest frequency
« Reply #3 on: February 15, 2021, 03:42:10 PM »
The annual average isn't that great for predicting the market.  For example if you take 1972-2020, the stock market averaged 10.65% per year... but it only returned near that amount once in 49 years.  The standard deviation of the market tends to be about +/- 15%, which is a much wider range than the question of annual vs daily compounding.