Compound Interest Calculator
Calculate future value, principal, interest rate, or time using the compound interest formula A = P(1 + r/n)nt. Supports daily, monthly, quarterly, and continuous compounding.
| Variable | Value |
|---|
| Solve For | Formula |
|---|---|
| Total Amount (A) | A = P(1 + r/n)^(nt) |
| Principal from A | P = A / (1 + r/n)^(nt) |
| Principal from I | P = I / ((1 + r/n)^(nt) – 1) |
| Rate (r decimal) | r = n * ((A/P)^(1/(nt)) – 1) |
| Rate (R percent) | R = r * 100 |
| Time (t) | t = ln(A/P) / (n * ln(1 + r/n)) |
| Continuous Amount | A = P * e^(rt) |
| Continuous Rate | r = ln(A/P) / t |
| Continuous Time | t = ln(A/P) / r |
| Frequency | Periods Per Year (n) | Description |
|---|---|---|
| Continuously | Infinite | Theoretical maximum; uses A = Pe^(rt) |
| Daily (365) | 365 | Common for high-yield savings accounts |
| Daily (360) | 360 | Used in some banking calculations |
| Weekly | 52 | 52 compounding events per year |
| Biweekly | 26 | Every two weeks |
| Semimonthly | 24 | Twice per month |
| Monthly | 12 | Most common for loans and credit cards |
| Bimonthly | 6 | Every two months |
| Quarterly | 4 | Common for bonds and certificates |
| Semiannually | 2 | Twice per year |
| Annually | 1 | Once per year |
What Is Compound Interest?
Compound interest is interest calculated on both your original principal and on interest that has already accumulated. With compound interest, your balance grows faster over time because each interest payment is added to the total balance before the next calculation begins.
For example, if you deposit $10,000 at 5% annual interest compounded monthly, you earn interest not just on the original $10,000 but on the growing balance each month. After 10 years that account can grow to over $16,470 without any additional deposits.
Compound vs Simple Interest
Simple interest uses the formula I = P x r x t and always calculates against the original principal only. Compound interest reinvests earned interest so the growth is exponential rather than linear. Over long time periods the difference becomes very significant. At 6% annual interest over 30 years, $10,000 grows to $17,908 with simple interest but to $60,226 with monthly compounding.
How Compounding Frequency Affects Growth
More frequent compounding means slightly more interest earned each year. The difference between annual and daily compounding on the same rate is modest but meaningful over decades. Continuous compounding represents the mathematical upper limit, using Euler’s number (e) in the formula A = Pe^(rt).
The Compound Interest Formula Explained
The compound interest formula is the core equation used by this calculator. The standard formula is written as:
A = P(1 + r/n)nt
Each variable plays a specific role:
- A is the final accrued amount including principal and all interest earned
- P is the starting principal, meaning the initial sum of money deposited or borrowed
- r is the annual nominal interest rate expressed as a decimal (so 5% becomes 0.05)
- n is the number of times interest compounds per year (12 for monthly, 365 for daily)
- t is the time in years (convert months by dividing by 12)
Solving for Other Variables
The formula can be rearranged to solve for any unknown. To find the required interest rate, the formula becomes r = n x ((A/P)^(1/(nt)) minus 1). To find how long it takes to reach a target amount, use t = ln(A/P) divided by (n x ln(1 + r/n)), where ln is the natural logarithm.
Continuous Compounding Formula
When interest compounds continuously, the formula simplifies to A = Pe^(rt). This uses Euler’s number e (approximately 2.71828) and represents the theoretical maximum growth for any given rate and time period. Most real-world accounts use discrete compounding rather than continuous compounding.
How to Use This Compound Interest Calculator
This compound interest calculator lets you solve for any one of five variables: total amount, principal (two methods), annual rate, or time.
Step by Step Instructions
- Select what you want to calculate from the “Calculate” dropdown at the top
- Enter values for all other fields (the field matching your selection will be left empty or ignored)
- Choose the compounding frequency from the dropdown
- Press Calculate or hit Enter to see your results
- The results panel shows the answer, a full breakdown, and the calculation steps
Converting Months to Years
The time field requires years. To convert months to years, divide by 12. For example, 18 months equals 1.5 years, and 30 months equals 2.5 years. You can enter decimals like 0.5 for six months or 0.25 for three months.
Practical Use Cases
- Estimate how much a savings account or CD will be worth at maturity
- Understand how credit card interest grows if only minimum payments are made
- Compare different bank accounts by calculating how different compounding frequencies affect returns
- Back-calculate the interest rate needed to reach a savings goal by a target date
- Determine how many years it will take for an investment to reach a specific amount
The Rule of 72 and Doubling Time
The Rule of 72 is a quick mental math shortcut for estimating how long it takes money to double at a fixed compound interest rate. Simply divide 72 by the annual interest rate percentage.
- At 4% annual interest: 72 / 4 = 18 years to double
- At 6% annual interest: 72 / 6 = 12 years to double
- At 8% annual interest: 72 / 8 = 9 years to double
- At 12% annual interest: 72 / 12 = 6 years to double
The rule is most accurate for interest rates between 6% and 10% and for annual compounding. For other compounding frequencies, you can use this calculator’s “Solve for Time” feature to get the precise doubling period.