Compound Interest Calculator
Calculate compound growth over time with optional regular contributions. Daily, monthly, quarterly, semiannual, or annual compounding with APY shown.
| Year | Balance | Contributions to date | Interest to date |
|---|---|---|---|
| 1 | $1,051.16 | $0.00 | $51.16 |
| 2 | $1,104.94 | $0.00 | $104.94 |
| 3 | $1,161.47 | $0.00 | $161.47 |
| 4 | $1,220.90 | $0.00 | $220.90 |
| 5 | $1,283.36 | $0.00 | $283.36 |
| 6 | $1,349.02 | $0.00 | $349.02 |
| 7 | $1,418.04 | $0.00 | $418.04 |
| 8 | $1,490.59 | $0.00 | $490.59 |
| 9 | $1,566.85 | $0.00 | $566.85 |
| 10 | $1,647.01 | $0.00 | $647.01 |
What this calculator does
This calculator projects the final balance and interest earned for any starting principal that compounds at a chosen frequency. Optional regular contributions are added each compounding period and themselves compound for the remaining periods. APY (the effective annual rate after compounding) is shown alongside the result. For fixed-term bank CDs, use the CD Calculator instead.
Formula
Lump sum: A = P × (1 + r/n)^(n × t)
With contributions (ordinary annuity): Acont = PMT × [((1 + i)^N − 1) / i]
Final balance: Total = A + Acont
APY: APY = (1 + r/n)^n − 1
Where i = r/n and N = n × t.
Variable definitions
P— Initial principal.PMT— Regular contribution per compounding period.r— Annual interest rate as a decimal.n— Compounding periods per year.t— Number of years.i— Periodic rate = r ÷ n.N— Total periods = n × t.APY— Effective annual yield after compounding.
Step-by-step calculation
- Compute
i = r / nandN = n × t. - Lump-sum balance:
A = P × (1 + i)^N. - Normalize the contribution to the compounding period (annual contribution ÷ n).
- Contribution balance:
Acont = PMT × [((1 + i)^N − 1) / i]. - Final balance = A + Acont. Interest earned = final − principal − total contributions.
Worked example
Principal = $1,000, rate = 5% annual, monthly compounding, 10 years, no contributions.
- i = 0.05 / 12 ≈ 0.004167; N = 120
- A = 1,000 × (1.004167)120 ≈ $1,647.01
- Interest earned ≈ $647.01
- APY = (1 + 0.05/12)12 − 1 ≈ 5.1162%
How to use this calculator
- Enter initial principal, annual rate, and years.
- Pick a compounding frequency (daily, monthly, quarterly, semiannual, annual).
- Optionally add a regular contribution and choose its frequency.
- Read the final balance, interest earned, total contributions, and APY.
Common mistakes
- Confusing nominal rate with APY: 5% compounded monthly produces ~5.12% APY — always compare on APY when shopping offers.
- Forgetting to convert percent to decimal: the calculator handles this internally; just enter the percent.
- Treating projections as guarantees: compound projections assume a constant rate; market returns vary.
Frequently asked questions
›What is compound interest?
Compound interest is interest that accrues on the original principal plus all previously earned interest. Because each period's interest itself earns interest, the balance grows faster than under simple interest.
›What is the compound interest formula?
A = P × (1 + r/n)^(n × t), where P is the principal, r is the annual rate as a decimal, n is the compounding periods per year, and t is the number of years. Total interest = A − P.
›What does compounding frequency mean?
It's how often interest is added back to the balance — daily, monthly, quarterly, semiannually, or annually. More frequent compounding produces slightly more interest at the same nominal rate, summarized by APY.
›What is APY?
Annual Percentage Yield is the effective annual rate after compounding: APY = (1 + r/n)^n − 1. APY lets you compare offers with different compounding frequencies on equal footing.
›How are regular contributions handled?
Contributions are added each compounding period and earn compound growth from that point forward. The calculator uses the future-value-of-an-annuity formula, paid at the end of each period (ordinary annuity).
›How is this different from the CD Calculator?
This page is general compound interest — any account, any term, optional contributions. The CD Calculator is modeled specifically for fixed-term bank certificates of deposit (single deposit, fixed APY, defined term).
›Does the calculator account for taxes or inflation?
No. Results are nominal pre-tax balances. Subtract expected inflation from the rate for a real-return view, and consult a tax professional for your specific situation.
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