$1,000 at 5% compounded annually for 2 years
$1,000 × (1.05)^2 = $1,102.50 future value; interest = $1,102.50 − $1,000 = $102.50.
Compound Interest Calculator
Estimate the future value of a starting amount with compound interest. Enter principal, annual rate, and years, then choose annually, quarterly, monthly, or daily compounding (monthly is the default). Optionally add a contribution at the end of each compounding period. Press Calculate for a cents-rounded future value, total contributions, and interest earned. This is investment-growth arithmetic, not financial advice.
Compound interest inputs
How compound interest results are calculated
This compound interest calculator finds future value with full precision, then rounds money to cents. Let r = annualRatePercent ÷ 100, n be compounds per year, and t be years. Total periods are N = n × t. N is used exactly even when it is fractional — the power (1 + r/n) ^ (n×t) is a real exponent (sometimes called the continuous exponent form). That is not continuous compounding P × e^(r×t). Daily compounding uses n = 365, not 365.25.
Future value of principal: FV_principal = P × (1 + r/n) ^ (n×t).
If contribution C > 0 per compounding period, deposits are an ordinary annuity (end of each period). If r === 0: FV_contrib = C × (n×t) — still linear when n×t is not an integer (a pro-rata partial period, not a requirement that the period count be whole). Otherwise FV_contrib = C × (((1 + r/n)^(n×t) − 1) / (r/n)). If C is 0, contribution timing is ignored and FV_contrib = 0.
total = FV_principal + FV_contrib. total deposits = C × n × t (again using the exact, possibly fractional, period count). interestEarned = total − P − (C × n × t). Each money output is then round-half-up to cents after that full-precision compute (same roundMoney approach as the discount calculator). Empty or non-numeric required fields, principal ≤ 0, a negative rate, years ≤ 0, a negative contribution, or an unknown frequency return a clear error instead of NaN.
Worked examples
$1,000 at 5% compounded monthly for 1 year
$1,000 × (1 + 0.05/12)^12 = 1051.161897881733… → round-half-up to $1,051.16 future value; interest $51.16 (not $1,051.17).
$1,000 at 0% monthly for 1 year with $100 per month
Rate 0: future value = $1,000 + $100 × 12 = $2,200.00; total contributions $1,200.00; interest $0.00.
Formula
r = annualRatePercent/100; n in {1,4,12,365}; N = n*t (exact, may be fractional); FV_principal = P*(1+r/n)^(n*t); if C=0: FV_contrib=0; if r===0 and C>0: FV_contrib = C*(n*t) (linear even if n*t is not an integer); else FV_contrib = C*(((1+r/n)^(n*t)-1)/(r/n)); total = FV_principal+FV_contrib; deposits = C*n*t; interestEarned = total-P-deposits; then round-half-up each money output to cents. Real exponent is not continuous compounding P*e^(r*t).
- P
- Principal / starting amount (must be > 0)
- r
- Annual rate as a decimal (annualRatePercent/100); 0 allowed, negative rejected
- n
- Compounds per year: annually 1, quarterly 4, monthly 12, daily 365
- t
- Years (must be > 0; fractional years allowed)
- N
- Total periods n×t, used exactly even when not an integer
- C
- Optional contribution per compounding period (default 0); end of period only
- deposits
- C×n×t, including a pro-rata amount when n×t is fractional
Not financial advice
This compound interest calculator is for general arithmetic only and is not financial, investment, tax, or professional advice. It does not forecast market returns, fees, taxes, or inflation. Results are rounded to cents and assume a fixed annual rate with optional end-of-period contributions. Verify figures with a qualified financial professional before making money decisions. GlobalToolHub assumes no liability for decisions made using these estimates.
Frequently asked questions
How does this compound interest calculator find future value?
Future value of the principal is P × (1 + r/n) ^ (n×t), where r is the annual rate as a decimal and n is how many times interest compounds per year. Optional contributions use the end-of-period (ordinary annuity) formula. Money is rounded to cents only after the full-precision total is computed.
What is $1,000 at 5% compounded monthly for one year?
With no contribution, $1,000 at 5% compounded monthly for 1 year is 1000 × (1 + 0.05/12)^12 = 1051.161897881733…, which rounds half-up to a future value of $1,051.16 and interest of $51.16. It is not $1,051.17.
How are contributions added?
A contribution greater than 0 is deposited at the end of each compounding period. If the rate is not zero, its future value is C × (((1 + r/n)^(n×t) − 1) / (r/n)). Total deposits equal C × n × t, including a pro-rata amount when n×t is not a whole number. A contribution of 0 ignores timing. Beginning-of-period deposits are not calculated.
What if the rate is 0% or the time is a fraction of a year?
A 0% rate is allowed. With $1,000, monthly compounding, 1 year, and $100 at the end of each month, future value is $1,000 + $100 × 12 = $2,200.00 and interest is $0.00. Fractional years are allowed: the exponent n×t is used as a real number, and at 0% the contribution piece stays C × n × t even when that product is not an integer.
Which compounding frequencies can I use?
Annually (n = 1), quarterly (n = 4), monthly (n = 12), and daily (n = 365). Monthly is the default. Any other frequency, including weekly or continuous compounding, returns an error. $1,000 at 5% compounded annually for 2 years with no contribution is a future value of $1,102.50 and interest of $102.50.
How are dollar amounts rounded?
Principal, contributions, future value, and interest are computed at full precision, then each money output is round-half-up to 2 decimal places (cents), the same roundMoney approach as the discount calculator. Example: the monthly 5% case rounds 1051.16189… to $1,051.16.
Is this financial advice, and why does principal 0 fail?
No. This page is general arithmetic, not financial, investment, or tax advice. Principal must be greater than 0, so principal 0 returns an error. A negative rate, years of 0 or less, a negative contribution, and an unknown frequency also return a clear error instead of NaN.