Future Value of Cash Flows Calculator: FV & PV by Year

How the future value of uneven flows works

An annuity formula only works when every payment is the same. Uneven flows have to be handled one by one: each year’s cash flow is grown to the end separately, and the grown amounts are added. The future value of the flow in year t is the flow times one plus the rate, raised to the number of years left after it — for the five default flows at 7%, the year-1 $1,000 has four years left, so it is $1,000 times 1.07 to the power of 4, which is $1,310.80; the year-5 $2,000 has no years left, so it stays $2,000.00. The present value is the mirror image: each flow is divided by one plus the rate, raised to its year — the year-1 $1,000 is $1,000 divided by 1.07, which is $934.58, and the year-5 $2,000 is $2,000 divided by 1.07 to the power of 5, which is $1,425.97. The interest earned is the future value minus the total cash in: $8,424.20 minus $7,500.00 is $924.20.

The per-year schedule

Every year’s flow, its growth factor, and what it becomes — at 7%, end of year.

The worked example, line by line

Setup: flows $1,000, $1,200, $1,500, $1,800, $2,000, rate 7% a year, end of year.

Line 1 — year 1, FV. $1,000 × 1.07^4 = $1,000 × 1.3108 = $1,310.80. PV: $1,000 / 1.07 = $934.58.

Line 2 — year 2, FV. $1,200 × 1.07^3 = $1,200 × 1.2250 = $1,470.05. PV: $1,200 / 1.07^2 = $1,048.13.

Line 3 — year 3, FV. $1,500 × 1.07^2 = $1,500 × 1.1449 = $1,717.35. PV: $1,500 / 1.07^3 = $1,224.45.

Line 4 — year 4, FV. $1,800 × 1.07 = $1,926.00. PV: $1,800 / 1.07^4 = $1,373.21.

Line 5 — year 5, FV. $2,000 × 1.07^0 = $2,000.00. PV: $2,000 / 1.07^5 = $1,425.97.

Line 6 — the totals. FV: $1,310.80 + $1,470.05 + $1,717.35 + $1,926.00 + $2,000.00 = $8,424.20. PV: $934.58 + $1,048.13 + $1,224.45 + $1,373.21 + $1,425.97 = $6,006.34.

Line 7 — the interest. $8,424.20 − $7,500.00 = $924.20 earned over five years.

Every branch, checked

Equal payments, 5 × $1,500 at 7%: the five FV terms are $1,966.19, $1,837.56, $1,717.35, $1,605.00 and $1,500.00, which add to $8,626.10; the five PV terms are $1,401.87, $1,310.16, $1,224.45, $1,144.34 and $1,069.48, which add to $6,150.30. Equal payments beat the uneven defaults on both measures, because the same $7,500 total arrives earlier on average — the uneven flows are back-loaded, with the biggest payment last.

At 10%: the five FV terms are $1,464.10, $1,597.20, $1,815.00, $1,980.00 and $2,000.00, which add to $8,856.30; the five PV terms are $909.09, $991.74, $1,126.97, $1,229.42 and $1,241.84, which add to $5,499.06. A higher rate lifts the future value and shrinks the present value — the same money is worth more later and less now.

Negative year-3 flow (−$500, others as default): the year-3 term becomes −$500 × 1.1449, which is −$572.45 of future value, so the FV is $6,134.40; the PV term becomes −$408.15, so the PV is $4,373.74. One bad year costs $2,289.80 of future value and $1,632.60 of present value — a negative flow is a cost in that year, and it compounds like any other flow.

At 0%: every factor is 1, so every term is the flow itself: FV = PV = $7,500.00. With no interest, future and present value are both just the total cash in, and the interest earned is $0.00. The 0% case is the sanity check: if a calculator does not return the plain total at 0%, its factors are wrong.

Ten yearly flows of $1,000 at 7%: the ten FV terms run from $1,838.46 for year 1 down to $1,000.00 for year 10, and they add to $13,816.45; the ten PV terms run from $934.58 down to $508.35, and they add to $7,023.59. Ten thousand dollars in, $13,816.45 out — $3,816.45 of interest, because the early flows compound for up to nine years.

Beginning-of-year timing at 7%: every flow arrives one year earlier, so every flow compounds one year longer: the FV is $9,013.89 and the PV is $6,426.79. The FV is exactly the end-of-year FV times 1.07 — $8,424.20 times 1.07 is $9,013.89 — and the PV is the end-of-year PV times 1.07 too. Timing matters: a year of growth on the whole stream is worth $589.69 of future value.

What the defaults assume

The defaults are five end-of-year flows of $1,000, $1,200, $1,500, $1,800 and $2,000 at 7% a year — a rising stream, like a side income that grows. The rate is one constant rate for all five years: no rate changes, no inflation adjustment, and no taxes. The flows are entered as end-of-year amounts unless the timing is switched to beginning-of-year. A negative flow is allowed and means money going out in that year — a cost, a repayment, or a loss — and it is discounted and compounded exactly like a positive flow. The calculator does not annualise or average anything: it grows and discounts each flow on its own, which is the only correct way to handle uneven flows.

Rounding convention, stated plainly: each discounted and compounded term is rounded to cents first, then the terms are summed — so the year-2 PV term is $1,048.13 and the five PV terms add to $6,006.34. The equal-payments FV terms are $1,966.19, $1,837.56, $1,717.35, $1,605.00 and $1,500.00, which add to $8,626.10. If the unrounded terms were summed first and rounded once at the end, the equal-payments FV would read $8,626.11 — one cent higher — so this page states its convention and sticks to it: round each term, then add.

Output · formula · meaning

Who uses this

• The growing side income: earns $1,000, then $1,200, then $1,500, $1,800 and $2,000 over five years, and learns the stream is worth $8,424.20 in five years and $6,006.34 today at 7% — with the per-year schedule showing which year does the work.
• The settlement recipient: is offered uneven instalments and learns what the stream is worth today — $6,006.34 at 7% — so the offer can be compared against a lump sum.
• The finance student: works through uneven cash flows by hand and checks each term against the schedule: $1,310.80, $1,470.05, $1,717.35, $1,926.00 and $2,000.00 of future value, $934.58 through $1,425.97 of present value.
• The business analyst: values a project with uneven yearly cash flows, including a negative year — a −$500 year 3 cuts the FV to $6,134.40 and the PV to $4,373.74 — and sees the cost of the bad year in both directions.

Accuracy & limitations

The math is exact for the numbers you enter: each flow’s future value is the flow times one plus the rate, raised to the years left after it; each flow’s present value is the flow divided by one plus the rate, raised to its year; the totals are the rounded terms summed; the interest is the future value minus the total cash in. But the inputs carry the assumptions. The rate is one constant rate for all five years — real rates move, and a rate that changes year to year needs a different calculation for each year. The flows are end-of-year unless the timing is switched, and the timing changes every term: beginning-of-year flows are worth $9,013.89 of future value against $8,424.20, so entering the wrong timing is a $589.69 mistake. A negative flow is treated as money going out in that year, which is the standard treatment, but a real project’s negative year may also carry tax or financing effects this calculator does not count. The rounding convention is stated above — round each term to cents first, then add — and the one-cent difference it makes against rounding once at the end is named in the worked example, so the figures can be checked by hand. No studies or statistics are cited on this page, because none are needed: every figure is arithmetic on the numbers you enter.