# ELI5. Compound interest

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Compound interest eli5:

Hello,

So I am little confused, I know that compound interests is interests on interests. But how you achieve it? Say that I invest 100 dollars in a Roth IRA in a eft fund that pays 2% dividends, after a year it grows to 102 dollars(plus appreciation with is like 7%) so like after a year I “have” around 110 dollars and as years go on this cycle repeats? Is this what compounding is in ROTH Ira?

In: Economics

You don’t “achieve” it, as much as it just happens. Your Roth IRA will “reinvest” the “earned” money back into itself. That “reinvested” money is the bases for additional earnings, which is why your earnings grow. Using earnings to make more earnings is the “compound” of compound interest.

So long as you’re not taking money out of the Roth, your interest/earnings will continue to grow.

Yes, and 110 dollars gets you about 11 dollars next year instead of 10 because you have an additional 10 dollars in it. Next year that is 12.1 dollars, etc.

Make sure you enable dividend reinvestment though.

So ETFs don’t pay interest, they pay dividends. Those are different. Dividends can change from year to year, even quarter to quarter, based on things like companies’ performance. And they’re not set as a percentage of share price. A company may pay 25 cents/share, and pay the same whether their stock is at \$20 or \$50. And ETF’s values rise and fall on daily basis as the underlying shares do.

Compound interest is relevant to things like savings accounts where interest is more defined, paid on the principal amount and the principal only grows as interest comes in.

I’m not sure what that specific case is, but here’s the maths in general:

So, the idea with compound interest is that you get interest on interest. Say you had £100 in an account that got 20% interest each year, for 5 years. The naïve approach would be to say you get 5 lots of interest, so you’d get an extra 5×20%=100%. But, each year, you gain interest, meaning the amount in the account that you earn interest on increases. After each year, you have 120% (or 1.2 as a decimal) of what you had the year before.

After year 1: 1.2×100=£120

After year 2: 1.2×120=£144

After year 3: 1.2×144=£172.80

After year 4: 1.2×172.8=£207.36

After year 5: 1.2×207.36=£248.83

You’ve got an extra £48.83 compared to linear interest (where you’d earn £20pa).

The quick way to calculate this is to work out the decimal version of what you have after each interest period (in this case 1.2), then raise it to the number of interest periods, then multiply that by the original amount.

So 100×1.2⁵=248.83.

When someone says compounding interest they’re talking about “how frequently the interest gets paid out and added back into the running total”.

Let’s say you have:
an interest rate of 10% ANNUALLY

The calculation is simple:
\$100 X 10%
\$110 TOTAL BALANCE

Alternatively, let’s say you have:
an interest rate of 2% ANNUALLY
your money compounds QUARTERLY [every 3 months]

The calculation is more complex:
\$100 X 10% X 3/12 months
\$100 + 2.50 interest

\$102.50 X 10% X 3/12 months
\$100 + 5.06 interest earned

\$105.06 X 10% X 3/12 months
\$100 + 7.69 interest earned

\$107.69 X 10% X 3/12 months
\$100 + 10.38 interest earned

\$110.38 TOTAL BALANCE

You’ll notice that it doesn’t make a huge difference. Unless you have a high interest rate [10% or more] or a high balance [\$1 million +] then daily compound interest doesn’t mean much compared to annual compounding interest.

For example,