Calculate Investment Growth
How Compound Interest Works
Compound interest is the eighth wonder of the world. It means you earn interest on your interest. When your investment generates returns and those returns themselves generate more returns, your money grows exponentially over time. The longer your money compounds, the more dramatic the growth becomes. This is why starting early is the single most important factor in building long-term wealth.
The Formula
For a lump sum with regular contributions, the formula is:
A = P(1 + r/n)^(nt) + PMT × ((1 + r/n)^(nt) - 1) / (r/n)
Where A is the final amount, P is the principal, r is the annual rate, n is compounds per year, t is years, and PMT is the monthly contribution.
Why AI Cannot Replace This Tool
Large language models frequently hallucinate compound interest calculations. They misapply formulas, confuse nominal and effective rates, mishandle contribution timing, and produce inconsistent results for the same inputs across different conversations. This tool uses deterministic JavaScript math with no approximation, no hallucination, and no variability. Every calculation is bit-exact and reproducible.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest which only earns on the principal, compounding creates exponential growth. The effect is minimal in early years but becomes dramatic over decades.
What compounding frequency should I choose?
Monthly compounding is the most common for savings accounts, 401(k)s, IRAs, and mortgages. Daily compounding earns slightly more (about $57 more per $10,000 at 7% over 10 years). The difference between monthly and daily compounding is usually minimal for long-term planning. Use the frequency that matches your actual account.
What is the difference between nominal rate and effective rate (APR vs APY)?
Nominal APR is the stated annual rate before compounding. Effective APY accounts for compounding frequency and shows the actual annual return. For example, 8% APR compounded monthly gives an APY of about 8.30%. Select Nominal if you know your account's stated rate; select Effective if you know the actual annual yield.
How much should I contribute monthly?
A common rule is 15% of your pre-tax income for retirement. Even small amounts matter: $100/month at 8% for 40 years grows to over $350,000. The most important factor is not the amount but the consistency and time horizon. Automate your contributions to build wealth steadily.
How long does it take for my money to double?
The Rule of 72 gives a quick estimate: divide 72 by your annual return rate. At 8%, money doubles every 9 years (72/8 = 9). At 10%, it doubles every 7.2 years. This rule works for any compounding frequency as a rough approximation.
Is this calculator accurate for real financial planning?
This calculator uses the standard compound interest formula that matches what banks and financial institutions use. However, real-world returns vary year to year, taxes may apply, and inflation reduces purchasing power. Use this as a planning tool, not a guarantee. Consult a financial advisor for personalized advice.
What is the snowball effect in investing?
The snowball effect describes how small investments grow into large sums over time, much like a snowball rolling downhill grows larger. In early years, most growth comes from your contributions. In later years, interest takes over and becomes the dominant growth driver. This calculator clearly separates contributions from interest so you can see when the snowball effect kicks in.
Does this tool save my financial data?
No. All calculations happen in your browser. Your financial data never leaves your device, is never stored on any server, and is never transmitted over the internet. This is 100% private. You can verify this by checking the Network tab in your browser's developer tools.
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