How compound interest is calculated
Compound interest is interest on interest: each period's interest is added to the balance, and the next period's interest is charged on the bigger total. The calculator runs month by month. It turns your annual rate and compounding frequency into the equivalent monthly rate, grows the balance, then adds that month's deposit.
Lump sum: A = P × (1 + r ÷ n)n × t
Equivalent monthly rate: m = (1 + r ÷ n)n ÷ 12 − 1
Each month: balance = balance × (1 + m) + deposit
Today's dollars = balance ÷ (1 + inflation)years
Here P is the starting amount, r the annual rate as a decimal, n the number of compounding periods a year and t the number of years. With monthly compounding, m is simply r ÷ 12.
Worked example: $10,000 plus $200 a month at 6% for 20 years
The monthly rate is 6% ÷ 12 = 0.5%. The $10,000 alone grows to 10,000 × 1.005240 = $33,102.04. The 240 deposits of $200 grow to $92,408.18. Together that is $125,510.22, from $58,000 of your own money. At 3% inflation, that balance is worth about $69,491.97 in today's dollars.
Look at the table: in year 10 the balance is $50,969.84, and less than a third of it is interest. By year 20 interest makes up more than half. Growth speeds up the longer the money stays put.
A quick check: the rule of 72
Divide 72 by the annual rate to estimate how many years money takes to double. At 6% that is about 12 years; at 8%, about 9. It is a rough guide, but it is a good way to sanity-check any growth projection you are shown.
Things to keep in mind
- Savings accounts and CDs pay a stated rate. Investments such as stock funds do not grow at a steady rate, so treat a fixed rate as an average, not a promise. The SEC's investor education site has its own compound interest calculator and explains the same idea.
- Taxes on interest and fund fees are not included. Both reduce what you keep.
- The inflation rate is the one you enter. Past U.S. inflation is published by the Bureau of Labor Statistics as the Consumer Price Index.
Questions people ask
How much will $10,000 grow to in 20 years?
At 6% compounded monthly, $10,000 on its own grows to $33,102.04 in 20 years. Add $200 a month and it reaches $125,510.22, of which $58,000 is your own money and $67,510.22 is interest.
Does compounding frequency matter much?
Less than people expect. $10,000 at 5% for 10 years ends at $16,288.95 compounded yearly, $16,470.09 monthly and $16,486.65 daily. The rate and the number of years matter far more.
What does the inflation-adjusted figure mean?
It is the future balance expressed in today's dollars: balance ÷ (1 + inflation rate) for each year. With 3% inflation, $125,510 in 20 years buys roughly what $69,492 buys today. Leave the inflation box empty to skip it.
Is the rate I enter an APY or an APR?
Enter the nominal annual rate and pick how often it compounds. If your bank quotes an APY (annual percentage yield), it already includes compounding, so enter it with yearly compounding to get the same result.
When are the monthly deposits added?
At the end of each month, so a deposit starts earning interest the month after it goes in. Your first year of $200 deposits therefore earns a little less than $2,400 × the rate.