Future Value Calculator — lump sum plus contributions

How it works

Two published formulas, summed. The lump: FVₚ = P(1 + r/k)^(k·y) — compound growth on the starting amount. The stream: FV_d = d((1+r/k)^(k·y) − 1)/(r/k) — the savings annuity on the contributions. The page adds them and then splits the result three ways: what the starting amount grew to, what you contributed in total, and the interest — everything above the money in. Zero either input and the page collapses to the pure case: the lump-only preset reproduces the $3,000-at-7% textbook example, the stream-only preset reproduces Tanya's quarterly deposits, both published values. The years sweep runs the combined plan at 5, 10, 20, and 30 years, where the interest line crosses the money-in line.

Worked example

Both anchors are LibreTexts' published cases, and both are presets here. The lump: $3,000 at 7% per year for four years grows to $3,932.39 (§8.02). The stream: $300 at the end of each quarter at 5.75% compounded quarterly reaches $5,353.89 in four years (§8.04). Combine the default inputs — $3,000 to start plus $300 a month at 7% for ten years — and this calculator's sum of the same two formulas reaches about $58,000, most of it contributions and roughly a third interest: its own composition of the two published pieces.

Frequently asked questions

What is future value?

Today's money projected forward at an assumed return: what a starting amount plus a contribution plan will be worth after a chosen number of years. It is the accumulation half of time-value-of-money; the present-value calculator runs the same arithmetic backwards.

Why are there two formulas inside?

Because the two kinds of money grow differently: the lump sum compounds for the whole horizon, while each contribution compounds only from the period it arrives. The closed forms handle both exactly, and their sum is the combined balance — no simulation needed.

How much of the result is interest?

The split outputs answer it directly: future value minus the starting amount minus total contributions. Early on, contributions dominate; the sweep shows the crossover year for your inputs, after which compounding contributes more than you do.

What rate should I assume?

The honest answer is a range, not a number: the rate is an assumption about future returns, and the result scales sharply with it on long horizons. Run a conservative and an optimistic figure and treat the spread — not either endpoint — as the projection.

Does contribution frequency matter much?

Less than rate and years: monthly contributions start compounding a little sooner than annual ones of the same yearly total, but the difference is small. Pick the frequency you will actually automate and let time do the heavy lifting.

How is this different from the savings and compound-interest calculators?

They are its two halves: compound-interest grows a lump sum alone, savings grows a deposit stream alone. This page is for the realistic case of both at once — an existing balance plus ongoing contributions — and it collapses to either sibling when one input is zero.

How accurate is this, and what does it exclude?

Exact for a constant rate, end-of-period contributions, and no withdrawals. It excludes market volatility, fees, taxes, and inflation — the future value arrives in future dollars, which buy less. For a goal in today's dollars, pad the target or discount the result with the present-value calculator.