What Is Compound Interest?
Compound interest is interest earned on both your original deposit and on the interest that has already accumulated. Simple interest only pays on the principal, but compound interest creates a snowball effect where your balance grows faster over time. The longer your money compounds, the more dramatic the growth becomes.
Consider a straightforward example. If you put $1,000 in an account earning 5% per year with simple interest, you earn $50 every year, and after 10 years you have $1,500. With compound interest, you earn $50 the first year, then $52.50 the second year because now you are earning interest on $1,050, then $55.13 the third year, and so on. After 10 years, you have $1,629 instead of $1,500. That extra $129 came from interest earning interest.
The Compound Interest Formula
The standard compound interest formula is:
A = P(1 + r/n)^(nt)
- A = final amount (future value)
- P = principal (initial investment)
- r = annual interest rate (as a decimal, so 7% = 0.07)
- n = number of compounding periods per year
- t = time in years
When you make regular monthly contributions, the formula adds a second component: A = P(1 + r/n)^(nt) + PMT x [((1 + r/n)^(nt) - 1) / (r/n)], where PMT is the payment per compounding period. This extended formula is what the calculator uses when you enter a monthly addition.
How $10,000 Grows Over Time
The table below shows how a one-time $10,000 investment grows at different annual rates with monthly compounding and no additional contributions. The differences across rates become more dramatic over longer time periods, illustrating why both the rate of return and the length of time matter so much.
| Annual Rate | 5 Years | 10 Years | 20 Years | 30 Years |
|---|---|---|---|---|
| 3% | $11,616 | $13,494 | $18,208 | $24,568 |
| 5% | $12,834 | $16,470 | $27,126 | $44,677 |
| 7% | $14,176 | $20,097 | $40,387 | $81,165 |
| 8% | $14,898 | $22,196 | $49,268 | $109,357 |
| 10% | $16,453 | $27,070 | $73,281 | $198,374 |
| 12% | $18,167 | $33,004 | $108,926 | $359,497 |
Source: Calculated using A = P(1 + r/n)^(nt) with P = $10,000, n = 12 (monthly compounding).
The key lesson: at 7% annual return, $10,000 roughly doubles every 10 years. After 30 years, the original $10,000 has grown to over $81,000, with more than $71,000 of that coming purely from compound interest. Use our percentage calculator to convert between decimal rates and percentages when comparing offers.
Compounding Frequency Comparison
How often interest compounds affects the total return, though the difference narrows as frequency increases. The table below shows how $10,000 at 6% grows over 10 years under each compounding frequency.
| Frequency | Periods/Year | Future Value | Total Interest |
|---|---|---|---|
| Annually | 1 | $17,908 | $7,908 |
| Semi-Annually | 2 | $18,061 | $8,061 |
| Quarterly | 4 | $18,140 | $8,140 |
| Monthly | 12 | $18,194 | $8,194 |
| Daily | 365 | $18,221 | $8,221 |
Source: Calculated using A = P(1 + r/n)^(nt) with P = $10,000, r = 6%, t = 10 years.
The jump from annual to monthly compounding adds $286 in interest, but moving from monthly to daily adds only $27. Most savings accounts and CDs compound daily or monthly, while many bonds and some loans compound semi-annually.
The Rule of 72
The Rule of 72 provides a quick mental shortcut for estimating how long it takes an investment to double. Simply divide 72 by the annual interest rate. At 6%, money doubles in approximately 72 / 6 = 12 years. At 8%, it takes about 9 years. At 12%, roughly 6 years.
This approximation works best for rates between 4% and 12%. It also works in reverse: divide 72 by the number of years to find the rate needed to double your money. If you want to double your investment in 10 years, you need roughly 72 / 10 = 7.2% annual return. To see the total return on an investment you have already made, try the investment return calculator.
The Power of Starting Early
Time is the most powerful factor in compound interest. Consider two investors at 7% annual return compounded monthly. Investor A starts at 25, invests $200 per month for 10 years (total: $24,000), then stops contributing but lets it compound until age 65. Investor B waits until 35, then invests $200 per month for 30 years straight (total: $72,000). By age 65, Investor A has approximately $393,000 while Investor B has about $243,000. Investor A contributed one-third as much money but ended up with 62% more, purely because of the extra 10 years of compounding.
Tom Brewer invested steadily in his 401(k) throughout his 35-year engineering career, contributing $300 per month. With an average annual return of 7% compounded monthly, that $300/month grew to over $530,000 by retirement. Of that total, he contributed $126,000 of his own money. The remaining $404,000 came from compound interest, meaning the market earned him more than three times what he put in. Tom uses this example when mentoring students in Pinewood Falls, emphasizing that starting early matters far more than the size of any single contribution.
You can plan specific savings targets with our savings calculator, or calculate loan payments to see how compound interest affects the other side of the equation.
This calculator provides estimates for informational purposes. It does not constitute financial advice. Actual investment returns vary based on market conditions and are not guaranteed. Consult a financial professional for decisions about your specific situation.