Compound Interest Calculator

A = P(1+r/n)nt — Calculate future value with regular contributions and see year-over-year growth.

Enter your values and click Calculate.

Understanding Compound Interest

Compound interest is the process of earning interest not only on your initial principal but also on all previously earned interest. Albert Einstein reportedly called it "the eighth wonder of the world." The mathematical formula is A = P(1 + r/n)nt, where:

  • A — the final amount (principal + all interest)
  • P — the principal (initial investment)
  • r — the annual interest rate (expressed as a decimal: 7% = 0.07)
  • n — the number of times interest is compounded per year
  • t — the time period in years

The Impact of Time

Time is the most powerful variable in compound interest. A $10,000 investment at 7% annual return grows to $19,672 after 10 years, $38,697 after 20 years, and $76,123 after 30 years. The money more than doubles every decade because the interest is itself earning interest. Starting early — even with a smaller amount — consistently outperforms starting late with a larger amount.

Regular Contributions

Adding regular contributions dramatically accelerates wealth accumulation. This calculator uses the future value of annuity formula to account for each contribution earning compound interest from the moment it is added. A $200/month contribution to a 7% account over 30 years adds an additional $242,000 in growth — on total contributions of only $72,000. The remaining $170,000 is pure compound growth on those contributions.

Compounding Frequency

More frequent compounding means interest is calculated and added to the principal more often, giving more opportunities for the new, higher balance to earn interest. For most practical purposes, the difference between monthly and daily compounding is small (a few tenths of a percent per year). The more significant choice is ensuring you are in an account that compounds at all — some savings products use simple interest.

Real-World Returns

Historical data shows the US stock market (S&P 500) has returned about 10% annually over the long term before inflation, or about 7% after inflation. High-yield savings accounts currently offer 4–5%. These rates fluctuate significantly year to year — the power of this calculator is in comparing scenarios, not predicting exact outcomes. Always consider that investment returns are variable and past performance does not guarantee future results.

The Rule of 72

A handy rule of thumb: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in approximately 12 years (72 ÷ 6). At 12%, it doubles in 6 years. At 4%, it takes 18 years. This works because the exact formula for doubling time is ln(2) / ln(1+r), which approximates to 0.693 / r ≈ 72 / (100r) for common interest rates.

Frequently Asked Questions

A = P(1 + r/n)^(nt). A = final amount, P = principal, r = annual rate (decimal), n = compounding periods per year, t = years. With regular contributions, the annuity formula is added to account for each payment's compound growth.
More frequent compounding slightly increases returns. $10,000 at 10% for 10 years: annually = $25,937; monthly = $27,070; daily = $27,179. The difference between monthly and daily is small, but annual vs. monthly can be significant.
Divide 72 by the annual interest rate to estimate doubling time. At 6%, money doubles in ~12 years. At 10%, ~7.2 years. At 4%, ~18 years.
No — it shows nominal returns. For real (inflation-adjusted) returns, subtract the inflation rate from your interest rate before calculating.
Each contribution earns compound interest from the day it is added. Small regular contributions (e.g. $200/month at 7% for 30 years) can grow to $242,000 — on $72,000 total paid in. The rest is pure compound growth.