What is the compound interest formula?

For discrete compounding: FV = P × (1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the time in years. With regular contributions (end of period): FV = P × (1+r/n)^(nt) + PMT × ((1+r/n)^(nt) − 1) / (r/n). For continuous compounding: FV = P × e^(rt).

How does compounding frequency affect growth?

The more frequently interest is compounded, the faster your money grows - but the effect diminishes at higher frequencies. Going from annual to monthly compounding makes a meaningful difference; going from daily to continuous is negligible. A $10,000 investment at 7% for 30 years: annually → $76,123; monthly → $81,745; daily → $81,822; continuous → $81,831.

What is continuous compounding?

Continuous compounding is the mathematical limit of increasing the compounding frequency to infinity. The formula is FV = P × e^(rt), where e ≈ 2.71828. While no real account uses continuous compounding, it's the theoretical upper bound and is used in some financial models.

What is the Rule of 72?

The Rule of 72 estimates how long it takes to double an investment: divide 72 by the annual interest rate. At 7%, your money doubles roughly every 72 ÷ 7 ≈ 10.3 years. At 6%, roughly every 12 years. It's an approximation - the calculator above gives the exact answer.

Does beginning vs. end of period matter for contributions?

Yes - contributions made at the beginning of each period earn one additional period of interest compared to end-of-period contributions. This is called an annuity-due (beginning) versus an ordinary annuity (end). The difference grows over long time horizons; for a $500/month contribution over 30 years at 7%, beginning-of-period contributions yield roughly 7% more.

Compound Interest Calculator - Future Value with Contributions

Year	Start balance	Interest	End balance	Total interest
1	$10,000.00	$700.00	$10,700.00	$700.00
2	$10,700.00	$749.00	$11,449.00	$1,449.00
3	$11,449.00	$801.43	$12,250.43	$2,250.43
4	$12,250.43	$857.53	$13,107.96	$3,107.96
5	$13,107.96	$917.56	$14,025.52	$4,025.52
6	$14,025.52	$981.79	$15,007.30	$5,007.30
7	$15,007.30	$1,050.51	$16,057.81	$6,057.81
8	$16,057.81	$1,124.05	$17,181.86	$7,181.86
9	$17,181.86	$1,202.73	$18,384.59	$8,384.59
10	$18,384.59	$1,286.92	$19,671.51	$9,671.51
11	$19,671.51	$1,377.01	$21,048.52	$11,048.52
12	$21,048.52	$1,473.40	$22,521.92	$12,521.92
13	$22,521.92	$1,576.53	$24,098.45	$14,098.45
14	$24,098.45	$1,686.89	$25,785.34	$15,785.34
15	$25,785.34	$1,804.97	$27,590.32	$17,590.32
16	$27,590.32	$1,931.32	$29,521.64	$19,521.64
17	$29,521.64	$2,066.51	$31,588.15	$21,588.15
18	$31,588.15	$2,211.17	$33,799.32	$23,799.32
19	$33,799.32	$2,365.95	$36,165.28	$26,165.28
20	$36,165.28	$2,531.57	$38,696.84	$28,696.84
21	$38,696.84	$2,708.78	$41,405.62	$31,405.62
22	$41,405.62	$2,898.39	$44,304.02	$34,304.02
23	$44,304.02	$3,101.28	$47,405.30	$37,405.30
24	$47,405.30	$3,318.37	$50,723.67	$40,723.67
25	$50,723.67	$3,550.66	$54,274.33	$44,274.33
26	$54,274.33	$3,799.20	$58,073.53	$48,073.53
27	$58,073.53	$4,065.15	$62,138.68	$52,138.68
28	$62,138.68	$4,349.71	$66,488.38	$56,488.38
29	$66,488.38	$4,654.19	$71,142.57	$61,142.57
30	$71,142.57	$4,979.98	$76,122.55	$66,122.55

Year

Start balance

Interest

End balance

Total interest

$10,000.00

$700.00

$10,700.00

$700.00

$10,700.00

$749.00

$11,449.00

$1,449.00

$11,449.00

$801.43

$12,250.43

$2,250.43

$12,250.43

$857.53

$13,107.96

$3,107.96

$13,107.96

$917.56

$14,025.52

$4,025.52

$14,025.52

$981.79

$15,007.30

$5,007.30

$15,007.30

$1,050.51

$16,057.81

$6,057.81

$16,057.81

$1,124.05

$17,181.86

$7,181.86

$17,181.86

$1,202.73

$18,384.59

$8,384.59

$18,384.59

$1,286.92

$19,671.51

$9,671.51

$19,671.51

$1,377.01

$21,048.52

$11,048.52

$21,048.52

$1,473.40

$22,521.92

$12,521.92

$22,521.92

$1,576.53

$24,098.45

$14,098.45

$24,098.45

$1,686.89

$25,785.34

$15,785.34

$25,785.34

$1,804.97

$27,590.32

$17,590.32

$27,590.32

$1,931.32

$29,521.64

$19,521.64

$29,521.64

$2,066.51

$31,588.15

$21,588.15

$31,588.15

$2,211.17

$33,799.32

$23,799.32

$33,799.32

$2,365.95

$36,165.28

$26,165.28

$36,165.28

$2,531.57

$38,696.84

$28,696.84

$38,696.84

$2,708.78

$41,405.62

$31,405.62

$41,405.62

$2,898.39

$44,304.02

$34,304.02

$44,304.02

$3,101.28

$47,405.30

$37,405.30

$47,405.30

$3,318.37

$50,723.67

$40,723.67

$50,723.67

$3,550.66

$54,274.33

$44,274.33

$54,274.33

$3,799.20

$58,073.53

$48,073.53

$58,073.53

$4,065.15

$62,138.68

$52,138.68

$62,138.68

$4,349.71

$66,488.38

$56,488.38

$66,488.38

$4,654.19

$71,142.57

$61,142.57

$71,142.57

$4,979.98

$76,122.55

$66,122.55

How to use the compound interest calculator

Enter your starting principal, expected annual interest rate, and investment period. Choose how often interest is compounded. Optionally add a monthly contribution. The future value, total interest earned, and a year-by-year breakdown update as you type.

The compound interest formula

For discrete compounding:

FV = P × (1 + r/n)^(nt)

where FV is the future value, P is the starting principal, r is the annual interest rate as a decimal, n is the compounding frequency (periods per year), and t is the time in years.

For continuous compounding:

FV = P × e^(rt)

With regular contributions (annuity), the future value of those deposits is added: PMT × ((1+r/n)^(nt) − 1) / (r/n) for end-of-period contributions.

The power of compounding: example

Principal	Rate	Years	Frequency	Future value
$10,000	7%	30	Annual	$76,123
$10,000	7%	30	Monthly	$81,745
$10,000	7%	30	Daily	$81,822
$10,000	7%	30	Continuous	$81,831

Why regular contributions matter

Adding a monthly contribution turns a modest starting balance into a substantial sum over time. A $10,000 starting balance at 7% over 30 years grows to about $76,000 on its own. Add a $500/month contribution and the total exceeds $680,000 (nearly 10× more), because every deposit also earns compound interest for the remainder of the investment period.

Compounding frequency comparison

More frequent compounding always produces a higher yield, but returns diminish quickly. Moving from annual to monthly compounding on a 7% investment makes a real difference (~7% more over 30 years). Moving from daily to continuous is negligible (<0.01%). Most real savings accounts compound daily or monthly; investment returns are often compared annually.

Inflation-adjusted (real) returns

A nominal return of 7%/year is not the same as a 7% increase in purchasing power. Inflation erodes the real value of your investment. The real return is approximately:

Real rate ≈ Nominal rate − Inflation rate

More precisely, using the Fisher equation:

Real rate = (1 + nominal) / (1 + inflation) − 1

At a 7% nominal return and 3% inflation, the real return is approximately 3.9%. Over 30 years, $10,000 grows to ~$76,000 nominally but only ~$32,000 in today's purchasing power. Always benchmark investment goals against inflation-adjusted projections.

Tax drag on compounding

Taxes reduce compounding in taxable accounts because a portion of gains is paid to the government each year, reducing the principal that compounds going forward.

Tax-deferred accounts (401k, Traditional IRA): contributions and growth are not taxed until withdrawal. The full principal compounds year-over-year, significantly increasing the ending balance compared to a taxable account with the same gross return.
Tax-free accounts (Roth IRA, Roth 401k): contributions are post-tax but growth and qualified withdrawals are never taxed again. Ideal for assets expected to appreciate significantly.
Taxable brokerage accounts: dividends and short-term capital gains are taxed as ordinary income each year. Long-term capital gains are taxed at lower preferential rates, but taxes still reduce the compounding base annually.