Compound Interest Calculator
Project future value with compound interest from principal, rate, compounding frequency, and time. Optional contributions. Runs locally in your browser.
Trust summary Engine tested · Specification checked · v1.1.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Future value of a lump-sum principal under compound interest, plus interest earned.
- Scope
- Constant nominal annual rate for the full term.
- Verification
- Engine tested · Specification checked · v1.1.0
- Named expert review
- Optional · Not performed
- Specification basis
- U.S. Securities and Exchange Commission (Investor.gov) — Compound interest explanation for investors
- Federal Reserve Bank education materials — time value of money and compounding frequency
- Standard actuarial / CFA TVM identity: FV = P(1 + r/n)^(n·t)
Formulas
Core equations used by this calculator.
How to use
Enter the principal
Starting amount P you invest or save today.
Set rate, years, and frequency
Annual rate in percent, time in years, and compounds per year (e.g. 12 for monthly).
Read future value and interest
See ending balance and interest earned (FV − P).
Example calculations
Common configurations with formula and result.
Monthly for 10 years
P = 1,000 · 5% · 10 yr · n = 12
Annual compounding
Same inputs with n = 1
Daily compounding
Same inputs with n = 365
Interest earned (monthly case)
FV − P
Common compounding frequencies (n)
Common values at a glance.
| Frequency | n (times / year) |
|---|---|
| Annually | 1 |
| Semi-annually | 2 |
| Quarterly | 4 |
| Monthly | 12 |
| Weekly | 52 |
| Daily | 365 |
Compound Interest calculator specification
Version 1.1.0 · Engine tested
- Engine tested 3 published cases
- Named expert review Not performed
- Calculation version 1.1.0
- Definition
- Compound interest is interest earned on both the original principal and on interest that has already been added to the balance. Over time the balance grows at an increasing rate. This calculator finds future value FV = P × (1 + r/n)^(n·t) for a lump-sum principal with a fixed annual rate and compounding frequency.
- What it calculates
- Future value of a lump-sum principal under compound interest, plus interest earned.
- Inputs
- Principal P (≥ 0)
- Annual rate in percent (≥ 0)
- Years t (≥ 0)
- Compounds per year n (≥ 1)
- Outputs
- Future value FV
- Interest earned (FV − P)
- Formula
FV = P × (1 + r/n)^(n·t); Interest = FV − P- Assumptions
- Constant nominal annual rate for the full term.
- Interest is compounded at a fixed frequency n with no deposits or withdrawals.
- No fees, taxes, or inflation adjustment.
- Calculation runs locally in the browser.
- Units
- Currency units for P and FV (any consistent unit)
- Rate in percent per year
- Time in years
- n as periods per year
- Boundary conditions
- n is treated as at least 1
- Negative principal or rate inputs are clamped to 0 in the tool
- Example
- P=1000, r=5%, t=10, n=12 → FV≈1647.01, interest≈647.01
- Validation cases
3 published on this page
- P=1000, 5%, 10 yr, n=12 → FV ≈ 1647.01
- P=1000, 5%, 10 yr, n=1 → FV ≈ 1628.89
- P=1000, 5%, 10 yr, n=365 → FV ≈ 1648.66
- Specification basis
- U.S. Securities and Exchange Commission (Investor.gov) — Compound interest explanation for investors
- Federal Reserve Bank education materials — time value of money and compounding frequency
- Standard actuarial / CFA TVM identity: FV = P(1 + r/n)^(n·t)
- Calculation version
- 1.1.0
Background
Interpretation and common distinctions.
What is compound interest?
Compound interest means you earn interest on your original principal and on interest that has already been added to the balance. Each compounding period, the base grows, so growth accelerates over time — the idea behind long-term savings, investments, and why unpaid debt can escalate.
Simple interest charges or pays interest only on the starting principal. Use the Simple Interest Calculator when that model fits; use this page when interest compounds.
Compounding frequency
For a fixed nominal annual rate, more frequent compounding raises effective growth slightly:
- 1 — annually
- 4 — quarterly
- 12 — monthly (common for savings)
- 365 — daily
When comparing products, look at APY (annual percentage yield) or effective annual rate — that already folds in compounding frequency.
Rule of 72
To estimate how long a balance takes to double at a steady rate:
Years to double ≈ 72/(annual % rate)
At 5%, about 72 / 5 = 14.4 years. Useful for mental math; use the full formula for planning.
What this tool does not include
- Recurring deposits or withdrawals (annuity / savings-plan formulas)
- Fees, taxes, or inflation
- Variable market returns
Results illustrate the compound-interest identity for a fixed rate and a single principal.
Related tools
Other calculators in this family: Simple Interest Calculator, Percentage Calculator .
Frequently asked questions
Key distinctions behind the calculation.
What is compound interest?
Compound interest is interest calculated on the principal plus any interest already credited. Each period you earn “interest on interest,” so growth accelerates compared with simple interest on the original principal alone.
What formula does this calculator use?
Future value FV = P × (1 + r/n)^(n·t), where P is principal, r is the annual rate as a decimal, n is compounds per year, and t is years. Interest earned is FV − P.
What is the difference between compound and simple interest?
Simple interest uses I = P × r × t on the original principal only. Compound interest reinvests earned interest, so the base grows each period. Over long horizons the gap becomes large.
Does compounding more often always help?
For a fixed nominal annual rate, yes — monthly beats yearly, and daily beats monthly — but gains get smaller as frequency rises. Always compare advertised APY or effective annual rate when shopping for accounts.
What should I enter for compounds per year?
Use 1 for annual, 4 for quarterly, 12 for monthly, 52 for weekly, or 365 for daily — matching how the account or loan compounds.
Can I include monthly deposits?
Not in this calculator. It models a single starting principal. For contributions each period you need a future-value-of-annuity (savings plan) formula in addition to the lump-sum term.
What is the Rule of 72?
A quick estimate of doubling time: years ≈ 72 ÷ annual percent rate. At 5%, money doubles in roughly 72 ÷ 5 ≈ 14.4 years. It is an approximation, not a substitute for the full formula.
Is this result financial advice?
No. Results are mathematical illustrations for a fixed rate with no fees, taxes, or market variability. Confirm terms with your institution and consider professional advice for real decisions.