Compound Interest Calculator
Compare interest compounding frequencies and convert nominal annual rates (APR) to effective yields (APY).
Wealth building principles
What Is Compound Interest?
Compound interest is interest earned on both the original principal and the interest that has already accumulated over time. In simple terms, compound interest means your money can earn money, and then that earned money can also earn more money.
A compound interest calculator helps you estimate how your savings or investments may grow. By entering your starting amount, regular contribution amount, rate of return, investment timeline, and compounding frequency, you can see how fast your wealth will accumulate.
Key variables
Anatomy of Compound Growth
Three main drivers dictate the final future balance of any compound calculation. Adjusting these parameters gives you a clear picture of how they interact.
- Starting Principal
- The initial lump sum deposit of your investment. A larger initial deposit sets a higher baseline for the compounding cycle to start.
- Regular Contributions
- Ongoing deposits made on a recurring basis (e.g. monthly or annually). Regular contributions fuel the compounding engine over time.
- Expected Return (Interest Rate)
- The annual growth rate. Historical stock market returns average around 7% to 10% before inflation, while savings accounts are lower risk but offer lower yield.
- Investment Timeline (Time)
- The number of years the money stays invested. Because compounding grows exponentially, time is the single most powerful factor.
- Compounding Frequency
- How often interest is calculated and added to the balance. Daily compounding yields slightly more than monthly or annual compounding.
- Inflation Rate Adjustment
- Adjusts future values into today's buying power. High inflation lowers the future purchasing power of your accumulated balance.
The mathematical model
Compound Interest Formula
Without recurring contributions, standard compound interest is modeled mathematically using:
Standard discrete compound interest formula
- A
- Final amount, also called future value.
- P
- Initial principal investment.
- r
- Annual interest rate written as a decimal.
- n
- Number of compounding periods per year, such as 12 for monthly.
- t
- Time in years.
Projection breakdown
Typical Compounding Growth Example
Let's look at a standard compound growth example: starting with $10,000, adding $200 monthly for 20 years at an expected 6% interest compounded monthly.
Growth comparison
Simple Interest vs. Compound Interest
Understanding the fundamental differences in how interest accrues:
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest Basis | Stated principal balance only | Principal + previously accumulated interest |
| Growth Pattern | Linear (constant amount every year) | Exponential (amount increases every year) |
| Standard Uses | Short-term notes, basic personal loans | Savings accounts, mutual funds, ETFs, 401(k) plans |
Fast estimate
The Rule of 72
The Rule of 72 is a simple mathematical shortcut to estimate the number of years required to double your investment at a given annual rate of return.
Years to double
For example, if your investment yields 8% annually, it will take approximately 9 years (72 / 8) to double in value without any additional contributions.
Related calculators
Comprehensive Wealth Calculators
Compounding acts as the foundational engine for all long-term savings structures. Connect your strategy to specific accounts.
Frequently Asked Questions
Compound interest is interest calculated on the initial principal plus all of the accumulated interest from prior periods. Essentially, it is interest on interest.
Yes. The more frequently interest compounding occurs, the higher the effective yield. Daily compounding produces slightly more growth than monthly, and monthly produces more than annual.
APR (Annual Percentage Rate) represents the simple nominal interest rate per year without compounding. APY (Annual Percentage Yield) represents the actual effective return over a year, taking the effect of compounding into account.
Yes. High-yield savings accounts (HYSAs) compound interest frequently (usually daily or monthly) and are advertised as APY. This calculator will help you project your savings over several years.
Inflation reduces the purchasing power of your money. A final value of $100,000 in 20 years will buy less than $100,000 today. Our calculator uses an inflation field to show you your projected balance in 'today's dollars'.
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