Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It allows your wealth to grow exponentially rather than linearly. The formula is A = P(1 + r/n)^(nt), where P is principal, r is rate, n is compounding frequency, and t is time.

The "Eighth Wonder of the World" visualized for your personal savings.

Formula

A = P(1 + r/n)^(nt). Total Balance = Principal * (1 + Annual Rate / Compounding Frequency)^(Frequency * Years).

How It Works

Input your initial investment (principal) and monthly budget.
Set your expected annual return and time horizon.
Choose how often the interest compounds (monthly is common).
Analyze the growth curve and see when interest overtakes contributions.

Formula:

Future Value = [Principal * (1 + r/n)^nt] + [Monthly Contribution * (((1 + r/n)^nt - 1) / (r/n)) * (1 + r/n)]

Examples

$10,000 principal at 7% for 20 years with $200 monthly contributions.

Result: $137,285 total balance. Over $80k earned in compound interest.

$1,000 start at 10% for 30 years with $100 monthly contributions.

Result: $211,385 total balance. The small monthly additions created massive wealth.

$0 start at 12% for 40 years with $500 monthly contributions.

Result: $5,142,520 total balance. Power of early consistency.

Frequently Asked Questions

What is the "Rule of 72"?

It is a quick way to estimate how long it takes to double your money. Divide 72 by the annual rate (e.g., 72 / 7% = ~10.3 years).

Does inflation impact these results?

Yes. To see "real" purchasing power, subtract the inflation rate (usually 2-3%) from your expected return (e.g., use 5% instead of 8%).

Is compound interest always a good thing?

For investments, yes. For debt (like credit cards), compound interest works against you, making the debt harder to pay off.

Which compounding frequency is best?

More frequent compounding (daily vs. monthly) results in higher returns, although the difference between monthly and daily is usually small.

What is a realistic interest rate for stocks?

The historical average for the S&P 500 is roughly 10% before inflation, or 7-8% after inflation.

Key facts

Compound interest accelerates wealth accumulation by earning "interest on interest". Time is the most critical variable; starting 5 years earlier can double the final outcome in many scenarios. Common compounding frequencies include monthly (12/yr), quarterly (4/yr), and annually (1/yr). Real-world returns are often estimated using market averages of 7-10% before inflation.

Trend & Behavior Analysis

As the time horizon (X-axis) extends, the curve of your wealth growth (Y-axis) becomes steeper. This "inflection point" usually occurs between years 15 and 25, where interest earned begins to exceed your annual contributions.