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How does the compound interest concept vary between a basic savings account and an index fund?

I understand compound interest as it relates to a basic savings account. If you get 5% interest on $1000 each year, it will be worth $1,050 at the end of the year, as $50 in interest was added. Over time it will keep compounding. Investing $1,000 in an S&P index fund will go up and down, which is not exactly the same as compounding. It may go up way more than 5%, but can that really be considered compound interest? 

Banking, Investing, Mutual Funds
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March 2016

Compounding really refers to earning money on the money that comes from an investment.  It’s easy to understand with things, like CDs, that pay a fixed amount of interest each year.  But with a stock or a mutual fund you need to be able to distinguish between changes in share value and the change in the number of shares you own due to dividends or interest payments that go into buying more shares.

In the case of a mutual fund where distributions are reinvested in more shares, compounding does work since each added share will be earning more dividends and capital gains.  Where it gets confusing is that this compounding can be masked by changes in share value, either up or down. 

So, from my perspective, compounding does apply to a both a mutual fund and a savings account but the math to determine the rate of return is much more complicated.

March 2016