Real saving rarely follows a neat schedule. A freelancer sets aside different amounts each year, a family deposits tax refunds and bonuses when they arrive, a business banks irregular surpluses. When the amounts vary, the annuity formulas no longer apply — each deposit has to be grown forward on its own. This calculator does exactly that and shows how much every individual amount contributes to the final balance.
How to use the calculator
- Type the cash flows in order, one per line, starting with period 1. Use 0 for a period with nothing and a minus sign for withdrawals. Shorthand such as
2000x5repeats an amount. - Enter the interest rate the money earns, as an annual effective rate.
- Choose whether each period is a year, quarter or month; for shorter periods the annual rate is converted to the equivalent periodic rate.
- Choose whether amounts arrive at the end or the start of their periods.
The table lists each cash flow with the number of periods it grows, its growth factor, its value at the end date and the running balance.
Formula for uneven cash flows
With cash flows CF1 … CFN at the end of each period and rate r per period:
The last cash flow earns nothing because it arrives on the end date; the first earns N − 1 periods. For start-of-period timing, each exponent increases by one.
Worked example
Over six years you save $5,000, $6,500, nothing, $8,000, $4,000 and $7,500 at the end of each year, earning 5%.
| Year | Deposit | Years of growth | Value at end of year 6 |
|---|---|---|---|
| 1 | $5,000 | 5 | $6,381.41 |
| 2 | $6,500 | 4 | $7,900.79 |
| 3 | $0 | 3 | $0.00 |
| 4 | $8,000 | 2 | $8,820.00 |
| 5 | $4,000 | 1 | $4,200.00 |
| 6 | $7,500 | 0 | $7,500.00 |
Future value: $34,802.20, of which $31,000 is deposits and $3,802.20 is interest. If each deposit were made at the start of its year, the total would be $36,542.31.
The running balance view
The last column of the calculator’s table tracks the account balance year by year: $5,000 after year 1, $11,750 after year 2, $12,337.50 after the empty year 3, and so on. Both methods — compounding each deposit to the end, or rolling the balance forward period by period — reach the same total, which makes a handy check on hand calculations.
Where this calculation is used
- Irregular personal saving: bonuses, side income and refunds.
- Business planning: projecting the value of retained earnings or a reserve fund built from variable surpluses.
- Finance coursework: “future value of a mixed stream” problems, where the table here mirrors the textbook layout.
- Terminal value in MIRR: the modified internal rate of return compounds positive cash flows forward to the end exactly this way — see the IRR calculator.
A short quarterly example: $2,000 deposited, $1,500 withdrawn, then two $3,000 deposits, at 4% a year, finishes at $6,559.56 after four quarters.
If every amount is the same, the future value of annuity calculator is quicker. To value an uneven stream in today’s dollars instead, use the present value of cash flows calculator.
Results assume a constant rate across all periods and are estimates for planning and study, not financial advice.
Frequently asked questions
How do you calculate the future value of uneven cash flows?
Compound each cash flow separately to the end date and add the results: FV = Σ CF_k × (1 + r)^(N − k) for end-of-period amounts. Unlike an annuity, there is no shortcut formula because the amounts differ.
What if some periods have no cash flow?
Enter 0 for those periods so the later amounts stay in the right positions. Each cash flow's growth depends on how many periods remain after it.
Can I include withdrawals?
Yes. Enter withdrawals as negative numbers. They are compounded forward the same way, reducing the ending value by what the withdrawn money would have earned.
How is this related to the present value of the same cash flows?
Future value equals present value times (1 + r)^N. For the example on this page, a present value of $25,969.94 at 5% grows to $34,802.20 after six years.
What does the start-of-period option do?
It treats every amount as arriving at the beginning of its period, so each one earns one extra period of interest. In the example, that raises the future value from $34,802.20 to $36,542.31.