📈 Compound Interest Calculator

🔧 Mode

📝 Account details

📤 Summary

{{ primarySummary }}
Enter account details — your future value and totals will appear here.

📊 Headline metrics

Final amount {{ formatMoney(finalAmount) }}
Total contributions {{ formatMoney(totalContributions) }}
Total interest {{ formatMoney(totalInterest) }}

🗂️ Period schedule

Showing the first 12 and last 12 periods. Download the CSV for the full schedule ({{ scheduleRows.length }} rows).

Period Interest Contribution Balance

📅 Year-by-year breakdown

Year Balance Interest earned Contributions to date
{{ row.year }} {{ formatMoney(row.balance) }} {{ formatMoney(row.interestEarned) }} {{ formatMoney(row.contributionsToDate) }}
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ℹ️ About Compound Interest Calculator

What is compound interest?

Compound interest is interest earned on both the original principal and on the interest previously accumulated. Each compounding period, the existing balance — including past interest — earns another round of interest. Over long horizons this effect produces the dramatic curves familiar from savings, retirement, and investment growth charts.

This calculator computes the future value of a starting principal under a constant annual rate, optionally with a regular contribution paid in every period. Use it to project savings balances, compare retirement scenarios, or sanity-check a financial product's stated return.

The compound interest formula

With a one-off principal P, an annual rate r (as a decimal), n compoundings per year, t years, and a periodic contribution PMT, the future value A is: 

A = P · (1 + r/n)^(n·t)
  + PMT · [((1 + r/n)^(n·t) − 1) / (r/n)] · (1 + r/n · {start: 1, end: 0})

P    = principal (starting balance)
r    = annual interest rate as a decimal (5% → 0.05)
n    = compoundings per year (1, 2, 4, 12, 365)
t    = term in years
PMT  = per-period contribution (monthly input is converted internally)

The second factor at the end of the contribution term handles the timing convention — see Contribution timing below. For a zero-rate scenario the formula collapses to A = P + PMT · n · t.

Common use cases

  • Retirement projection: $0 today, $500/month for 30 years at 7% compounded monthly grows to roughly $610,000.
  • Savings goal: back-solve how long $10,000 takes to double at 4% APY (≈ 18 years; the Rule of 72 gives 72/4 = 18).
  • Education fund: model an 18-year college fund with monthly contributions.
  • Down-payment plan: see how a high-yield account differs from a regular savings rate.
  • Investment comparison: compare effective yield of products quoted with different compounding frequencies.

Compoundings per year

Compoundings per year is how often interest is calculated and added back to the balance. More frequent compounding produces a slightly higher effective yield for the same nominal rate.

  • 1 — annually: interest credits once a year. Common for some bonds and CDs.
  • 2 — semi-annually: twice a year. Common for many fixed-income securities.
  • 4 — quarterly: four times a year. Common for older savings accounts.
  • 12 — monthly: twelve times a year. Common for mortgages, HYSAs, and money market accounts.
  • 365 — daily: credited every day. Common for modern online savings accounts and credit cards.

For a 5% nominal rate, daily compounding produces about a 5.127% APY versus 5.000% for annual — small per year, meaningful over decades.

Contribution timing: start vs end

When you contribute PMT every period, the timing convention matters for the future value:

  • End of period (annuity-immediate, default): the deposit lands at the end of each compounding period, so it earns interest starting next period. This matches how most retirement accounts and direct-deposit savings work.
  • Start of period (annuity-due): the deposit lands at the beginning of the period, so it earns interest this period. Common for rent payments, insurance premiums, and some pension contributions.

Mathematically the start-of-period future value is exactly (1 + r/n) times the end-of-period value — one extra period of interest on every contribution. Over 30 years at 7% monthly compounding, the start convention yields about 0.58% more.

Modes

  • Compute: final amount, total contributions, total interest, and a per-year breakdown.
  • Schedule: the full period-by-period table — every period's interest, contribution, and balance. Download as CSV for spreadsheets.

References

Notes

  • Results are illustrative; real-world accounts may include fees, taxes, or rate changes that this tool doesn't model.
  • Calculations run entirely in your browser unless you call the API endpoint below.
  • The same TypeScript logic powers the API — you'll get identical results from either path.

API Usage Example:

POST /api/tools/math/compound-interest-calculator
Content-Type: application/json

{
    "operation": "compute",
    "principal": 10000,
    "annualRatePercent": 5,
    "years": 10,
    "compoundingsPerYear": 12,
    "monthlyContribution": 0,
    "contributionTiming": "end"
}
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