How compound interest works
With simple interest, you earn returns only on the money you put in. With compound interest, the returns are reinvested and earn returns of their own. Year after year, the growth grows: that is the snowball effect Albert Einstein is (probably wrongly) credited with calling the eighth wonder of the world.
For a lump sum, the formula is A = P × (1 + r)n, where P is the starting balance, r the annual rate of return and n the number of years. With regular contributions, each monthly payment compounds for the time remaining, and the calculator adds them all up using the exact equivalent monthly rate.
A worked example
Invest $10,000, then add $500 a month for 10 years at 7% a year. You contribute $70,000.00 in total and end up with $105,197.38: $35,197.38 of growth. With 2.5% inflation, that balance is worth $82,180.02 in today's money.
Keep going for 30 years and the picture changes completely: $190,000.00 contributed becomes $660,848.85, and growth now makes up 71% of the balance. Time, not the amount saved, is the most powerful ingredient.
Start early: the cost of waiting
Someone who invests $300 a month from age 25 to 65 (40 years) at 7% contributes $144,000.00 and retires with $741,462.60. Someone who waits until 45 and invests twice as much, $600 a month for 20 years, contributes the same $144,000.00 but ends up with only $304,521.83. The early saver has $436,940.78 more for the same effort.
Fees: the silent drag on compounding
Fees compound too, against you. On the 30-year example, a 1% annual fee cuts the final balance from $660,848.85 to $544,691.40, a loss of $116,157.45. Low-cost index funds with expense ratios under 0.1% keep almost all of the growth for you.
Timing matters a little as well: contributing at the start of each month rather than the end adds one month of growth to every payment, worth $3,306.13 over 30 years in our example.
Taxes and tax-advantaged accounts
The tax field applies a single rate to the total growth when you withdraw. In a Roth IRA, a UK ISA or a Roth 401(k), growth is tax-free: leave it at 0%. In a taxable brokerage account, long-term gains are taxed at 0%, 15% or 20% in the US (see our capital gains tax calculator) and at 18% or 24% in the UK (see the UK CGT calculator). In practice, dividends are also taxed every year outside these accounts, which slows compounding slightly.
Limits of the projection
The calculator assumes a constant rate of return every year. Real markets go up and down, and the order of returns matters, especially close to retirement. Treat the result as an order of magnitude, test several rates, and remember that past performance does not guarantee future results.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on interest. Each year, the returns of your investment are added to your balance and start earning returns themselves. The longer you stay invested, the more this snowball effect dominates: after a few decades, most of the balance usually comes from growth rather than from the money you put in.
What is the rule of 72?
Divide 72 by the annual rate of return to estimate how many years it takes to double your money. At 6% a year, money doubles in about 12 years; at 9%, in about 8 years. It is a quick approximation of the exact formula ln(2) / ln(1 + r).
What rate of return should I use?
Use a conservative long-term assumption. Broad stock market indexes such as the S&P 500 have returned roughly 10% a year on average over long periods before inflation, with large swings from year to year and no guarantee for the future. Bonds and cash have returned much less. Many planners use 5% to 7% for a diversified portfolio, then subtract fees.
Why does the calculator convert the annual rate to a monthly rate?
Contributions are made every month, so growth is calculated monthly. Dividing the annual rate by 12 would overstate the result, because monthly growth also compounds. The calculator uses the exact equivalent monthly rate, (1 + annual rate)^(1/12) − 1, so that twelve months of growth give exactly the annual rate.
How much do fees matter?
A lot over long periods. With $10,000 invested plus $500 a month for 30 years at 7%, a 1% annual fee reduces the final balance by about 18%. Enter your fund expense ratio or advisory fee in the fees field to see the difference.
What does "in today's money" mean?
It is the final balance adjusted for inflation: what it would buy at today's prices. With 2.5% inflation, $100 in 20 years has the purchasing power of about $61 today. It is the most meaningful figure for long-term goals like retirement.
Educational tool: not financial, tax or investment advice. Results are estimates based on the assumptions you enter and on official rates at the date shown. Investments can fall as well as rise. For decisions about your own situation, speak to a qualified adviser or tax professional. Read the full disclaimer.