Compound Interest Calculator

Compound interest adds earnings to an interest-bearing balance so earlier earnings can generate further growth. The result depends on starting principal, rate, duration, compounding convention and any deposits along the way.

This investment growth calculator explores a hypothetical constant-rate scenario. It separates your own savings from modeled earnings, rather than presenting every increase as investment performance. A smooth projection does not imply a guaranteed return.

1. Select a currency for formatting and enter the starting investment, including zero if you plan to begin with deposits.
2. Enter the nominal annual interest rate from 0% to 100%. Do not substitute an already effective annual yield.
3. Set whole years and optional additional months. Six months represent half a year; the total limit is 200 years.
4. Select annual, semiannual, quarterly, monthly or 365-period daily compounding.
5. Optionally enable monthly deposits and choose beginning or end timing.
6. Review the result, chart and yearly table. Open frequency and simple-interest comparisons for more detail.

Results update instantly. Copy, print and CSV include the assumptions. Reset restores 1,000 principal, 5% nominal interest and two years of annual compounding, with contributions and inflation disabled. Currency amounts support two decimal places; changing currency does not exchange funds.

For a lump sum, A = P × (1 + r/n)^(n × t). P is starting principal, r is the nominal annual rate as a decimal, n is periods per year and t is years. The result A includes principal and interest.

For example, 5% becomes 0.05, monthly compounding sets n = 12, and eighteen months sets t = 1.5. Without deposits, interest is A − P. With deposits, subtract both principal and all additional contributions. Intermediate growth retains precision rather than rounding every credit to cents.

For 1,000 at an illustrative 5% compounded annually for two years: 1,000 × 1.05² = $1,102.50. Interest is $102.50.

For 5,000 at 6% nominal, compounded monthly for five years: 5,000 × (1 + 0.06/12)^60 = $6,744.25, including $1,744.25 interest. The monthly periodic rate is 0.5%; the effective annual yield is 6.1678%.

These examples use the interactive calculator’s engine. Rates are assumptions, not current offers or predictions.

Annual compounding has one period per year, semiannual two, quarterly four, monthly twelve and daily 365 here. Holding a positive nominal rate constant, more frequent compounding generally increases effective annual yield.

The comparison panel changes only frequency. Principal, nominal rate, duration and deposit schedule stay the same. Its period count is n × t, including any fractional final period; it is not a count of completed credits.

This model uses 12 equal months and 365 equal days per year. A month therefore spans 365/12 model days. There are no leap dates or changing calendar-month lengths. A bank’s actual daily-balance and posting methods may produce different results.

For monthly compounding with end-of-month deposits, FV = P × (1+i)^N + PMT × [((1+i)^N − 1)/i], where i = r/12, N is months and PMT is the monthly deposit.

Starting with 1,000, adding 100 each month for twelve months at 6% nominal with monthly compounding produces $2,295.23. Total contributed is $2,200.00 and interest is $95.23.

For beginning timing, the deposit annuity term receives an extra factor of (1+i), while the principal term stays unchanged. This example then finishes at $2,301.40.

For other frequencies, the engine processes monthly deposits and credit events explicitly. Between events it uses geometric fractional-period growth, including growth on accrued interest. Accrued earnings are tracked separately until credited; posting them does not increase the balance a second time. This geometric extension is a modeling assumption and differs from a bank accruing simple daily interest only on posted balances.

The final value includes accrued but uncredited interest at the chosen horizon. When material, that amount appears in the result notes.

The annual example earns 50 in year one. Year two begins with 1,050, so 5% earns 52.50. The extra 2.50 arises because the first year’s earnings remained in the account.

Longer time allows more repeated growth, but the rate actually experienced still matters. This page assumes a constant nonnegative nominal rate; it does not simulate changing or negative market performance.

Simple interest on a lump sum uses A = P × (1 + r × t). For the same 1,000 at 5% for two years, the simple balance is $1,100.00, compared with $1,102.50 under annual compounding: a $2.50 difference.

The comparison also handles identical monthly deposits. Each deposit earns simple interest only on its principal for the remaining time; earned interest is not reinvested. Deposits are never quietly removed from one side of the comparison.

Over a partial credit period, geometric fractional-period growth can be lower than prorated simple interest. The result depends on the adopted fractional-period convention.

Effective annual yield describes one year’s compounding effect: APY = [(1 + r/n)^n − 1] × 100%.

At 5% nominal with monthly compounding, APY is 5.11618979%, displayed as 5.12% APY. It describes money invested for a full year, not an identical return on every deposit regardless of arrival date.

The nominal input divides into periodic rates before compounding. Effective annual yield includes the resulting within-year growth. An already effective yield should not be entered as a nominal rate, which could overstate growth.

Actual APR and APY disclosures may follow product-specific fee and timing rules. This model does not implement every disclosure standard. For a certificate-of-deposit estimate accepting APY directly, use the CD Calculator.

Regular deposits raise principal and give each payment its own opportunity to grow. The calculator separately reports initial principal, additional deposits, total contributed and earnings.

At zero interest, 1,000 plus twelve deposits of 100 equals 2,200; all growth comes from saving. With no initial investment, growth starts only after a deposit arrives. An end deposit at the final horizon is included but earns no interest.

At zero duration there are no scheduled monthly deposits, even under beginning timing. Future balance equals the initial principal.

The chart uses the engine’s actual monthly account balance, cumulative contributions and accumulated earnings. Contributions include initial principal. The balance minus contributions represents modeled earnings.

Hover, touch or focus the chart to inspect a month. Arrow keys move between months; Home and End select endpoints. The yearly table provides a text alternative and includes partial final years.

Balances round to cents for display. Each table interest cell is the balancing difference between rounded ending balance, starting balance and deposits. This makes displayed rows, successive years and the final result reconcile exactly, while intermediate growth remains unrounded. CSV includes both unrounded summary values and the reconciled table.

A nominal future balance is a future currency amount. Its purchasing-power equivalent today uses future nominal value ÷ (1 + inflation rate)^years.

For example, 10,000 in five years at an assumed 3% annual inflation corresponds to $8,626.09 today. The optional input starts at an illustrative 3%, not a claimed current inflation statistic.

The adjustment does not change the nominal account balance, contributions or interest. It is a purchasing-power illustration, not an additional investment return.

Regular periods: 12 equal months and 365 equal days per year. Geometric fractional-period accrual at log(1 + r/n) per credit period includes accrued interest between credits. Monthly deposits occur at the selected boundary; credit events post accrued interest without adding it twice. Final value includes uncredited accrual. No actual calendar dates, taxes, fees or market variation.

Input limits are 1 billion initial principal, 10 million monthly deposits, 200 years and a 0–100% nominal rate. Projections above 1 trillion currency units are withheld to retain useful numerical precision. Negative rates, withdrawals, taxes and fees are outside this model.

• CFPB: compound interest and an annual worked example
• Investor.gov: savings, deposits and compounding inputs

These references explain general compounding. The explicit equal-period geometric event convention is this calculator’s modeling choice, not a claim about a financial institution’s rules.