# How does compounding interest work with a retirement fund?

Asked by

rjb1983 (

158
)
January 27th, 2011

I’m a bit confused here. People say that if you have $10,000 in a retirement account, the interest will compound over time, leaving a sizable nest egg from which to retire. Now, I get how compounding interest works with loans, mortgages, etc. because of the recapitalization—in that the interest gets added on to the principal every month, and then interest gets added on to *that* increased principal, etc. and the process repeats until you make regular payments which exceed the interest assessment on that principal.

But with an IRA or 401k, it seems that the total value is always tied to the number of shares you have and the per-share value of the stock/mutual fund you own. So it seems that you wouldn’t take advantage of compounding interest, because your gains are never recapitalized back into your “principal investment.” It would seem then that the gains would be fairly linear over time. I suppose I don’t get how just leaving $10k in an investment account with medium risk (let’s say 15%) is going to grow at more than a simple linear rate without any recapitalization.

Any help would be appreciated!

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## 6 Answers

In the case of a mutual fund investment (which is where I presume that your 401(k) is invested), the growth of the mutual fund itself is (or should be) compounding. That is, the fund takes profits from time to time (we hope) from realized gains due to its own trading activities, and your share of those profits (since they won’t be distributed to you) are reinvested in the fund. So your investment grows because the value of the fund’s shares increases due to its internal compounding, and reinvestment of dividends, if any.

In the case of a self-directed IRA (or any stock account, generally) you may elect to have dividends reinvested in shares of stock (partial shares) that actually increase your holdings over time, with no additional overt purchases from you.

Your missing one essential piece. Some stocks pay dividends. That will generally be reinvested and used to buy more stocks. Also stocks will split, doubling the number of shares. And finally, 401’s are generally put into funds. A stock fund is a basket of stocks some may pay dividends, some may pay interest. The fund manager buys and sells stocks to rid them of under performing stocks and buys higher performing stocks. All those things will make the fund increase in value annually. And those increases are reinvested compounding your return.

So to sumarize:

1) value of underlying stocks/bonds go up

2) dividends/interest are paid from the underlying stocks/bonds

Remember your money is in a larger pool of money growing together where continuous adjustments (buy sell decisions) are occuring where new payments by you and dividend dispursements are continuously being reinvested.

You and four other people pay $1 in, so you start with $5 in the fund owning 5 stocks. After a a month the fund investments pay a dividend of $0.20/stock or $1 total, which is reinvested buying another stock so fund is worth $6 with 6 stocks. The value of the companies underlying stocks grow by by $1/stock so the fund is now worth $12 . Fund manager sells all and is holding $12.

He finds another stock worth $1 and buys 12 shares. In a month dividend of $0.20/stock for a total of $2.40. The fund buys two more stocks costing $1.20 each. The fund is worth $14.40 in 14 stocks. The stocks grow by $1 per stock, so the fund is worth $28.40. The fund manager sells it all and has $28.40.

He finds another stock costing a $1 and buys 28 shares. and so on and so on and so on.

Get it

What you are forgetting is that is 15% (or whatever) per year represents the total value of the investment. So, in effect it does get added to your principal.

Simple 15% interest on $10K is 1500 per year So

Year1 – 11500

Year2 – 13000

Year3 – 14500

etc…

However, when that interest stays (due to the higher value of the investment)

Year1 – 15000

Year2 – 13225

Year3 – 15208.75

etc…

@YoBob What do you mean by “when that interest **stays**”?

What I mean is that if you purchase a stock at $100 per share, if it goes up by 15% then it is worth $115 per share. Then, if it goes up another 15% the next year that 15% is on the $115 value, not the original $100 purchase price.

So, in effect the interest gets applied to your “principal” (aka. the absolute value of your stock)

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