Future Value of Regular Payments

This calculator answers one question in depth: what does a stream of regular payments become? Not a lump sum, not a lump sum with deposits attached — the payment stream itself. That is the classic future value of an annuity problem, and it behaves differently from a single deposit because each payment compounds for a different length of time. The first one earns almost the whole horizon; the last one earns nothing at all.

Because the stream is the subject, everything that shapes a stream is a first-class input. How often you pay in. Whether the money arrives at the start of the period or the end. Whether the payment stays flat for twenty-five years or rises with your income. Each of those is worth a specific amount of money, and this page puts a figure on each rather than describing it in the abstract.

If your question is really about a starting balance — an amount you already hold, with or without deposits on top — the general future value calculator is the right tool and it is linked below. This page deliberately keeps the payment stream in the foreground, and treats a starting balance as an optional extra rather than the main event.

Start with the split. The headline is the ending balance; underneath it, total contributions and total growth divide that figure into money you supplied and money the return assumption supplied. On a twenty-five year monthly plan at 6%, contributions are 43% of the ending balance and growth is 57%. Run the same payment for five years and contributions are 86% of it. That is why the growth share tells you more about a plan than the headline figure does.

Then read the three comparison tables, because each answers a question a basic annuity calculator leaves open. The timing table prices the difference between paying at the start and the end of each period. The escalation table prices an annual increase, including how much extra you pay in to get it. The scenario table shows how much of the projection depends on the return you assumed rather than on your saving.

The escalation table appears even when your plan is level: in that case it shows what a 3% annual increase would add, clearly labelled as an illustration. The point is that the comparison is available before you have to guess whether it is worth modelling.

Finally, the schedule. The yearly view carries a payment column, which is where an annual increase becomes visible year by year. The per-payment view drops to one row per contribution, and its final row closes on exactly the headline figure.

For a level payment stream the calculation has a closed form. Each payment compounds from the moment it is made to the end of the horizon, and summing that geometric series gives the annuity factor — one multiplier applied to the payment. The calculator prints this closed-form figure alongside the schedule whenever the payment is level, so the two can be checked against each other.

Once the payment steps up each year, that single factor no longer applies. Closed forms do exist for particular growing-annuity cases, but they assume the payment grows every period at the same rate the balance compounds at — not an annual step-up applied to payments made monthly, with a compounding frequency that may differ and a part-year at the end. Rather than print a formula the code does not run, the Quantus model accumulates the balance deterministically, payment by payment, so one code path handles annual step-ups, mixed frequencies and part-year horizons alike. That iterative result is the source of truth whenever the annual increase is above zero.

Part-year horizons are resolved to whole payments: 2.5 years of monthly payments is 30 contributions, never 30.5. Balances are carried at full precision through the schedule and rounded to cents only for display, so the per-payment view, the yearly view and the headline figure all reconcile.

Take $500 a month for 25 years at a 6% nominal return compounded monthly, paid at the end of each month. The monthly rate is 0.005 and there are 300 payments, so the annuity factor is (1.005^300 − 1) / 0.005 = 692.994 and the future value is $346,496.98. You paid in $150,000; the remaining $196,496.98 — 56.7% of the balance — is growth.

Move the same payments to the start of each month and the result becomes $348,229.47. The gain is $1,732.49, or 0.50% — exactly one month at the periodic rate, applied to every payment. It costs nothing but a change of transfer date.

Now apply a 3% annual increase instead. The payment rises from $500 to $515 in year two, $530.45 in year three and $1,016.40 by year 25. Total contributions rise to $218,756 and the ending balance to $461,679. The $68,756 of extra contributions produced $115,182 of extra value — $1.675 for every additional dollar, because the early increases still had two decades left to compound.

The table below isolates a different lever: the same $6,000 a year, split into payments of different sizes. Nothing about the money changes, only when it arrives — and the spread between the best and worst arrangement is $18,595.