How compound interest works
Compound interest is interest on interest. Each period the balance earns its rate, and that growth is added to the balance, so next period's growth is a little larger. Over short spans it looks like simple interest. Over decades the growth on past growth becomes the larger part of the total, which is why starting early matters more than almost any other choice.
Start with $10,000, add $500.00 at the end of each month and earn 7% a year, compounded monthly. After 20 years the balance is $300,851. Your deposits total $120,000; growth is $170,851, 56.8% of the balance. The starting $10,000 on its own would have become $40,387.
| Year | Balance | Deposits so far | Growth so far |
|---|---|---|---|
| 5 | $49,973 | $30,000 | $9,973 |
| 10 | $106,639 | $60,000 | $36,639 |
| 15 | $186,971 | $90,000 | $86,971 |
| 20 | $300,851 | $120,000 | $170,851 |
Time matters most
The same plan over 10 years ends at $106,639, and over 30 years at $691,150. Someone who starts ten years later, with nothing saved and the same $500.00 a month, has $86,542 by the same date. The rule of 72 gives a quick check: divide 72 by the yearly return to get roughly how many years money takes to double, about 10 years at 7%. Depositing at the start of each month instead of the end adds a month of growth to every deposit and ends at $302,370.
Where compounding works for you, and against you
The same arithmetic runs on debt. A credit card balance left unpaid compounds at the card's rate, which is usually far above anything savings earn, so clearing it is the best return available. Inflation compounds too: it quietly shrinks what a fixed sum buys, year after year.
For savings, the choice of account sets the rate. A high-yield savings account or a certificate of deposit pays a stated rate and is insured up to the federal limit. Bond and stock funds have no fixed rate; their long-run returns have been higher but come with years of losses along the way. A tax-advantaged account, such as a 401(k) or IRA, lets the growth compound without yearly tax, which adds up over decades; the retirement calculator adds an employer match.
What the inputs mean
- Starting balance: what you have saved today.
- Deposit and how often: a regular monthly or yearly amount, at the start or end of each period.
- Yearly return: before inflation and tax. Subtract expected inflation for a figure in today's dollars.
- Years and compounding: how long, and how often growth is added.
Common mistakes
- Using a high return because it was true last year. Long-term planning needs a figure that holds up in bad decades too.
- Forgetting inflation. A balance decades from now buys less than the same figure today.
- Ignoring fees. A fund fee comes off the return every year and compounds against you.
Compound interest questions
How much will $500.00 a month grow to?
With $10,000 to start and $500.00 added each month at 7% a year, about $300,851 after 20 years. You put in $120,000; the other $170,851 is growth. After 30 years it is $691,150.
Does compounding daily or monthly make much difference?
Less than people expect. On the example, yearly compounding ends at $292,465, monthly at $300,851 and daily at $301,636. The return rate and the years matter far more.
What is the difference between APR and APY?
APR is the yearly rate before compounding; APY is what you actually earn in a year once compounding is counted, so it is a little higher. Savings accounts advertise APY. Enter an APY here with yearly compounding, or an APR with the account's own compounding.
Should I deposit monthly or once a year?
Monthly, if you can. Money deposited earlier has longer to grow, and steady deposits are easier to keep up. In the example, depositing at the start of each month instead of the end ends at $302,370 rather than $300,851.
What return should I assume?
Use a cautious figure for anything long term. A savings account pays a known rate; stock funds have returned more over long periods but swing widely from year to year and can fall. At 4% instead of 7%, the example ends at $205,613 instead of $300,851.