Compound Interest Calculator

You start with a balance, add money every month, and let growth compound. This calculator projects that forward: the starting balance grows every month, and each monthly contribution starts growing from the month it lands. By default, contributions land at the endof each month — an “ordinary annuity”, the conservative, standard convention. Switch to beginning-of-month (an “annuity due”) and every deposit gets one extra month of compounding. Unlike most calculators, we state that convention instead of hiding it.

The growth rate you enter is an annual nominal rate (APR-style) at your chosen compounding frequency — not an effective annual yield. Because contributions are always monthly, the engine converts that nominal rate into the single equivalent monthly rate that produces the identical effective annual yield, so contributions and compounding live on one timeline. Under this model, deposits earn growth every month even when compounding is quarterly or annual — results will differ slightly from calculators that credit interest only at each compounding event (there, a mid-year deposit earns nothing until the credit date; here it earns the equivalent monthly rate immediately). Daily compounding uses a fixed 365-day year, ignoring leap years; the effect is a fraction of a basis point.

The optional annual contribution increase raises your monthly contribution once per year — modeling contributions that grow with your income. The year-by-year table splits each year into contributions and growth, in plain language, and its final row always equals the headline future value because both come from the same calculation.

Symbols: P = starting balance, C = monthly contribution, Y = years, r= growth rate ÷ 100, m = compounding periods per year, g = contribution increase ÷ 100, n = 12 × Y months, i = equivalent monthly rate.

i = (1 + r ÷ m)^m/12− 1 (when compounding is monthly this is exactly r ÷ 12)
futureValue = P × (1 + i)ⁿ + C × [((1 + i)ⁿ− 1) ÷ i]

In words: the principal grows by the monthly rate for every month, and the stream of end-of-month contributions grows by the standard future-value-of-an-ordinary-annuity factor — each deposit compounds only from the month after it lands. For beginning-of-month contributions, the contribution term is multiplied by one extra factor of (1 + i). When you set an annual contribution increase, the engine runs the same math year by year: each year’s ending balance compounds for 12 months and that year’s (raised) monthly contributions accumulate under the one-year annuity factor — this yearly recursion also generates the table, and with no increase it reproduces the closed-form formula exactly. When the rate is 0%, money simply accumulates without growth (the engine never divides by zero). Total contributed = P plus every dollar deposited; total growth = future value − total contributed. All intermediate balances are kept at full floating-point precision; only displayed values are rounded to cents.

$10,000 starting balance, $500/month, 8% annual growth, 10 years, monthly compounding, no contribution increase, end-of-month contributions:

1. Decimal rate: r = 8 ÷ 100 = 0.08. Monthly compounding, so i = 0.08 ÷ 12 = 0.0066667.
2. Months: n = 12 × 10 = 120.
3. Growth factor: (1 + 0.08/12)¹²⁰ = 2.2196402.
4. Principal part: $10,000 × 2.2196402 = $22,196.40.
5. Annuity factor: (2.2196402 − 1) ÷ (0.08/12) = 182.94603.
6. Contribution part: $500 × 182.94603 = $91,473.02.
7. Future value = $22,196.40 + $91,473.02 = $113,669.42.
8. Total contributed = $10,000 + ($500 × 120) = $70,000.00.
9. Total growth = $113,669.42 − $70,000.00 = $43,669.42.

Timing check: switching to beginning-of-month contributions multiplies the contribution part by (1 + 0.08/12): $91,473.02 × 1.0066667 = $92,082.84, so the future value becomes $114,279.24 — $609.82 more from one extra month of compounding per deposit.