Compound interest

Compound interest is interest that earns interest. When a bank credits interest to a savings account, the interest joins the balance and the next credit is computed on the larger figure; the same happens to a card balance that is carried, where the interest charged is added to what is owed. The growth is slow for years and then fast, because the interest is a percentage of a balance that the interest itself keeps enlarging. At 6% a year, $10,000 becomes $17,908 in ten years and $57,435 in thirty, and the second twenty years add five times what the first ten did.

In a sentence

• "At 6% a year, compound interest turns $10,000 into $57,435 over thirty years, and $29,435 of that is interest earned on interest."
• "Compound interest works for a saver and against a borrower; a carried card balance compounds the same way."
• "Most of the balance after thirty years of compound interest is growth rather than deposits, which is why the early years matter more than they look."

How it works

Balance after n periods = starting balance × (1 + rate per period)^n

1. The period's interest is computed on the whole balance, the original deposit plus every credit so far.
2. The interest is added to the balance rather than paid out.
3. The next period starts from the larger balance, so its interest is larger, by the interest on the interest.

Three inputs set the result: the rate, the number of periods, and how often interest is credited. Time does the most. Doubling the years does far more than doubling the rate, because the late years compound on everything the early ones built. Frequency does the least: 6% credited monthly is worth 6.17% credited yearly, and over decades the difference is a few percent of the total. Any growth left in the account compounds the same way, whether it is interest, dividends or appreciation, which is why the word is applied to whole portfolios.

An example

$10,000 at 6% a year, credited yearly, with no deposits or withdrawals, against the same $10,000 earning simple interest of $600 a year.

Simple interest pays $600 every year, on the original $10,000 only, and reaches $28,000 in thirty years. Compound interest pays $600 the first year and $3,251 the thirtieth, because the thirtieth year's 6% is computed on $54,184 rather than on $10,000. Of the $47,435 of compound interest, $18,000 is the same simple interest and $29,435 is interest on interest, and that second figure is almost nothing for the first five years. With a monthly deposit the same arithmetic runs on every contribution from the month it lands: $200 a month at 6% a year, credited monthly, is $200,903 after thirty years, of which $72,000 is deposits and $128,903 is growth.

Why it matters

Compound interest is the reason time is worth more than rate, and the reason a small balance started early beats a larger one started late. A saver who starts ten years sooner at the same $200 a month does not end up with ten years of extra deposits, $24,000, but with what those deposits and their interest produce over the extra decade, which at 6% is the difference between $92,408 after twenty years and $200,903 after thirty.

The mistake it prevents is judging the method by its first years, when the balance is small and the interest is a rounding error. The mirror image is debt: a card balance carried at 24.99% APR compounds against you by the same arithmetic, so the interest not paid this month is charged on next month.

Compound interest versus simple interest

Simple interest is computed on the original amount only; compound interest is computed on the original amount plus the interest already credited. Under simple interest a balance grows by the same dollar figure every period, a straight line, and under compound interest it grows by a rising figure, a curve. At 6% on $10,000 the two are identical in year one, $36 apart in year two and $29,435 apart in year thirty. Simple interest is rare on deposits, but it is how an amortized car loan or mortgage charges interest, on the current balance each month, and it never compounds there because each payment clears it. See APY for how compounding is quoted on a deposit and APR for how it is left out of a loan's rate.

Common questions

Is compound interest the same as APY? No, but APY is how compounding is quoted on a deposit account: the growth of the balance over one year with the compounding counted, so that a 4.00% rate credited monthly reads as a 4.07% APY. Compound interest is the mechanism, and APY is the yearly rate that results from it.

Does compound interest apply to debt? Yes. Interest charged on a carried card balance is added to the balance and charged on again, so a balance that is not paid down grows along the same curve a saving would. A card at 24.99% APR compounds daily, which is why a carried balance costs slightly more than the APR alone suggests.

How long does money take to double with compound interest? Divide 72 by the rate for a close estimate: about twelve years at 6%, ten at 7% and eighteen at 4%. The exact figure at 6% is 11.9 years. See Rule of 72.

Is investment growth compound interest? It is compound growth: dividends reinvested and gains left in the account produce further gains on a larger balance, the same arithmetic with a return that varies year to year instead of a stated rate. The curve has the same shape, and the line is bumpier.

Go deeper

• The Compound interest calculator shows how a starting balance and a monthly contribution grow at a given return over the years, and how much of the final amount is interest on interest rather than money you put in.
• The Retirement calculator projects what your retirement savings could grow to by the age you plan to stop working, what that is worth in today's dollars, and the monthly income it could support.
• Why net worth grows slowly at first and then faster runs twenty years at $800 a month and shows the share of each year's growth that comes from the balance rather than from you.

Where it shows up in Zypper

Zypper draws the curve as it happens. Savings accounts, including money market accounts and CDs, and investment and brokerage accounts connect and contribute their balances to net worth, which is computed from every account and charted over time; connected accounts update every day, so the flat early years and the steepening later ones are the same line viewed at different points. The transfers into those accounts are recognized as movements between your own accounts, which is the deposits column, and the growth is the rest of the line's rise. See Net worth tracking and Supported account types for the details, or get started with Zypper to see where on the curve you are.