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

Future value (end of period)
$6,202.50
3 cash flows ยท $6,000.00 undiscounted ยท $202.50 growth
  • Number of periods3
  • Sum of cash flows (no growth)$6,000.00
  • Period 1: $1,000.00 ร— (1+r)^2$1,102.50
  • Period 2: $2,000.00 ร— (1+r)^1$2,100.00
  • Period 3: $3,000.00 ร— (1+r)^0$3,000.00
  • Total future value$6,202.50
  • Interest earned$202.50
Not financial advice โ€” Assumes each cash flow arrives at the end of its period and compounds at a constant rate to the final period. For beginning-of-period (annuity-due) timing, multiply by (1 + r).

Step-by-step

  1. Each cash flow is compounded forward to the end of period 3 at 5% per period.
  2. FV = 1,000ร—(1+r)^2 + 2,000ร—(1+r)^1 + 3,000ร—(1+r)^0.
  3. Total future value = $6,202.50 ($202.50 of it is growth).

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 โ€” the first is treated as occurring at the end of period one โ€” 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 โ€” the formula

FV = ฮฃ_{t=1..n} CFโ‚œ ร— (1 + r)^(n โˆ’ 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.

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

Compound each cash flow forward to the end of the final period and add them up: FV = ฮฃ CFโ‚œ ร— (1 + r)^(n โˆ’ t). Earlier cash flows grow over more periods, so they contribute more than equal-sized later ones.

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