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If I take 100 dollars and put it into a savings account that pays me 5% annual interest which compounds monthly. At the end of the year I will have $105.12

If I take the same 100 dollars and invest it in a stock that does not pay dividends that grows 5% by the end of the year I will have 105 dollars.


However, if I take 100 dollars and put it into a savings account that pays me 5% annual interest compounded annually I will have 105 dollars.

Someone told me that compounding frequency does not have any bearing on the return on investment but these calculations seem to disagree as the ROI for savings would be 5.12 and the ROI for stock would be 5.

Is there something I am missing here? And if so, what?

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    Take a gander at APY vs APR – Hart CO Apr 7 at 3:40
  • Here's a quick comparison: studentloanhero.com/featured/apr-vs-apy – Hart CO Apr 7 at 3:47
  • These comments were somewhat helpful, but I am still having trouble understanding whether that person was right or wrong or whether we were just not talking about the same thing. What I think so far is I was talking about APR while they were talking about APY. – mcsc Apr 7 at 4:03
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Yes, compounding frequency does have an impact on your return. In general, more frequent compounding boosts your return.

The big proviso is that you have to leave the money invested in order for it to compound. In your savings account example, that's exactly what you're doing and the more frequent payout means that the interest is itself earning interest.

When you move into stocks, it isn't quite as clean-cut as that. There are fees to consider. In most of the accounts where I am, dividend reinvestment can be set to be automatic and low-cost, but even a low cost does eat into your return. The other thing is that you won't necessarily get an exact number of shares for your dividend (you might not even get any, depending on the share price), which will throw out the calculation.

Let's take a couple of simplified examples.

Stock A costs $1 per share and dividends $0.05 per annum. You buy $1000 of it and at the end of the year, you should have 1050 shares at $1 => $1050. But, your provider charges $1 for the reinvestment. So you have $1049.

Stock B costs $1 per share and dividends $0.0125 per quarter. You buy $1000 of it and at the end of the year, you have 1044 shares and $2.82 cash => $1046.82. Ouch, the fees ate more of your return.

Stock C costs $1 per share and dividends $0.05 per annum. You buy $10000 of it and at the end of the year you should have 10499 shares at $1 => $10499.

Stock D costs $1 per share and dividends $0.0125 per quarter. You buy $10000 of it and at the end of the year you should have 10504 shares with $1.36 cash => $10505.36. The more frequent compounding has overtaken the fees and improved your return.

Of course, the people who put together the sheets that describe stocks aren't unaware that a more frequent dividend will tend to result in a higher return, but they also can't know what your particular fees will be. So they ignore it and assume that you're just taking the cash each time.

All the stocks above yield a nominal 5%, but you can see from the final numbers that that's not what you're getting unless you just collect the cash.

  • But the question states that they "invest it in a stock that does not pay dividends". – mhoran_psprep Apr 7 at 12:05
  • @mhoran_psprep I was, perhaps incorrectly, assuming that the OP was doing that to keep it comparable to a simple annual savings account. I intentionally skipped over non-dividending shares and the share price because then you get into questions of ROE, ROCE and EV vs market capitalization. I'll happily take out the stock part if it's confusing the issue. – Greig Apr 7 at 13:20
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There is no such thing as a compound frequency in a stock investment. I have no idea how much my investments will be worth in a year.

Investing in stocks or mutual funds and money in a bank account are different. The price of a share doesn't move in a straight line, nor does it move in a staircase fashion with regular interest.

If the market expects the company have have growing sales of 10% and they report 9.9% today the price of a share might drop tomorrow. If the market expects sales to grow by 5% and they report 9.9% the price might jump tomorrow.

When you say you bought a $100 worth of shares and they are now worth $105 a share a year later that means if you sell them now, this instant, you will get $105 excluding commissions. But if you wait until tomorrow it could be higher or lower.

Your question was about non-dividend paying stocks. But even with a dividend the value doesn't move in any sort of a pattern. When they pay a dividend the money goes to you, and the price per share drops by essentially the same amount. If you re-invest the dividend the number of shares you own will go up with the dividends you receive, but at that moment the value of your investment doesn't move.

Keep in mind that the dividend is a separate item unrelated the the share price. The dividend is paid from company profits. But a company can have profits and still have a dropping share price.

This answer ignores taxes because the money in a bank account, or the money received by through a dividend might or might not be taxable.

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Someone told me that compounding frequency does not have any bearing on the return on investment but these calculations seem to disagree as the ROI for savings would be 5.12 and the ROI for stock would be 5.

If the investment pays interest (Savings, CD's, etc) then compounding frequency matters if they are reporting the interest you'll earn as APR (annual percentage rate). Many interest-bearing accounts show APY (annual percentage yield) which factors in compounding. If your savings account example above was 5% APY you'd have $105, if it was APR with monthly compounding you'd have $105.12

Stocks don't have compounding periods, so if you want to compare two investments you'll just want to frame both in terms of yield over the specific time period. You also wouldn't want to ignore taxes/commissions in a thorough comparison.

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