Compound Interest Calculator

What this calculator does

This calculator computes future value and interest earned when a sum (principal) grows at a given annual interest rate over a number of years, with a chosen compounding frequency: annual, monthly, daily, or continuous. All values are in the same currency as the principal.

It is useful for savings accounts, CDs, and long-term growth projections. Investors and savers use it to see how compounding frequency affects the result and to compare different rate/term combinations. It assumes a constant rate and no taxes or fees.

How to use it

1. Enter Principal—the amount you invest or deposit (e.g. $1,000).
2. Enter Annual interest rate as a percent (e.g. 5 for 5%).
3. Enter Years—the time horizon.
4. Choose Compounding frequency: Annual, Monthly, Daily, or Continuous.
5. Read Future value and Interest earned (future value − principal) in the Result section.

Inputs are in the left panel; the result updates as you change any value. Use the same currency for principal (e.g. all dollars).

Formulas used

• Discrete compounding (annual, monthly, daily):
  FV = P × (1 + r/k)^(k×t)
  where P = principal, r = annual rate (as decimal, e.g. 0.05 for 5%), k = compounding periods per year (1, 12, or 365), t = years.
  Interest earned = FV − P.
  More frequent compounding (e.g. monthly vs annual) yields slightly higher future value for the same rate and term.

• Continuous compounding:
  FV = P × e^(r×t)
  where e is the base of the natural logarithm (~2.718). Same r and t as above. Continuous compounding is the limit as k → ∞ and is used in some academic and financial models.

Interpretation & examples

• Example 1: $1,000 at 5% for 10 years, monthly → FV ≈ $1,647, interest ≈ $647.
• Example 2: Same ($1,000, 5%, 10 years) with continuous compounding → FV ≈ $1,649, interest ≈ $649. The difference from monthly is small but grows with rate and term.
• Example 3: $10,000 at 4% for 20 years, monthly → FV ≈ $22,254, interest ≈ $12,254. Useful for retirement or long-term savings planning.

Higher compounding frequency (e.g. monthly vs annual) yields slightly higher future value; continuous is the theoretical maximum for a given rate and term.

History & background

Compound interest has been used in finance and mathematics for centuries. Continuous compounding is common in academic finance and some derivatives pricing; banks and savings products typically quote and compound at discrete intervals (monthly, daily). This calculator supports both for comparison and education.

Limitations & safety notes

• Not financial or tax advice. Assumes a constant rate and no taxes or fees. Real accounts may have variable rates, fees, or tax on interest.
• Use for education and estimation only. Confirm actual rates and terms with your bank or broker. Past performance does not guarantee future results.