Future Value of Uneven Cash Flows Calculator

Compute the future value of a series of unequal cash flows compounded forward at a given rate to the end of the period.

Inputs

One value per period, comma-separated. The first occurs at the end of period 1.

Interest/return rate per period.

Result

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How to use this calculator

  • Enter your cash flows as a comma-separated list, one per period.
  • Enter the interest/return rate per period.
  • Read the total future value at the end of the last period.
  • See how each cash flow grows and the total interest earned.

About this calculator

Many real-world plans involve deposits or income that change from period to period rather than a fixed amount. This calculator finds the future value of such a stream of uneven cash flows by compounding each one forward to the end of the final period at a constant rate. A cash flow that occurs earlier earns interest over more periods, so it contributes more to the final total than a later one of the same size. Enter your cash flows as a comma-separated list — the first is treated as occurring at the end of period one — and a rate per period, and the tool sums the grown values, breaking out how much each flow becomes and how much of the total is interest. This is the building block behind retirement projections, irregular savings plans, and valuing variable income.

How it works — the formula

FV = Σ_{t=1..n} CFₜ × (1 + r)^(n − t) (first flow at end of period 1, valued at end of period n)

Each cash flow is grown by the number of periods between when it occurs and the final period, then summed.

Source: Investopedia — Future Value

Worked examples

Example 1
1000, 2000, 3000 at 5%
Inputs:
flows=1000,2000,3000; rate=5
Output:
1102.5 + 2100 + 3000 = $6,202.50
Example 2
500, 500, 500, 500 at 4%
Inputs:
flows=500,500,500,500; rate=4
Output:
$2,122.98 (level annuity)
Example 3
5000, -1000, 3000 at 6%
Inputs:
flows=5000,-1000,3000; rate=6
Output:
mixed deposit/withdrawal

Limitations

  • Ordinary-annuity timing (end of period); multiply by (1+r) for due.
  • Constant rate across all periods.
  • Breakdown lists the first 8 flows for readability.

Time-value calculation; assumes a constant periodic rate.

Frequently asked

How do you find the future value of uneven cash flows?+
Compound each cash flow forward to the end of the final period and add them up: FV = Σ CFₜ × (1 + r)^(n − t). Earlier cash flows grow over more periods, so they contribute more than equal-sized later ones.
When does the first cash flow occur?+
This tool uses ordinary-annuity timing, where the first cash flow occurs at the end of period one and the last at the end of period n (the valuation date). For beginning-of-period timing, multiply the result by (1 + r).
How is this different from a regular annuity?+
A regular annuity has equal payments; this handles different amounts each period. The future value of a level annuity is a special case where every cash flow is the same. Use this when deposits or income vary.
Why do earlier cash flows contribute more?+
Because they compound over more periods. A $1,000 deposit three periods before the end grows more than a $1,000 deposit one period before the end, since it earns interest for two extra periods.
Can I include negative cash flows?+
Yes — a negative value represents a withdrawal, which is compounded forward as a reduction to the future value. This lets you model streams that mix deposits and withdrawals.
What rate should I use?+
Use the rate that matches your period. For monthly cash flows, use a monthly rate (annual ÷ 12); for annual flows, an annual rate. The rate and the cash-flow periods must be on the same time scale.

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