Future Value Calculator

About the Future Value Calculator

Future value is the basic machinery of time and money: what an amount today, or a stream of payments, becomes at some rate over some period.

  FV = PV(1 + r)ⁿ + PMT · ((1 + r)ⁿ − 1)/r

The compound interest calculator covers growth and the savings calculator covers what the result is worth. What neither answers is the question this one exists for: what does the timing cost?

Not the rate. Not the amount. The when.

How to Use the Future Value Calculator

Enter an amount today, what you add each period, the rate and the number of years. Either the lump or the contribution can be zero.

Compounds sets the period. Contributions are paid chooses between the end of each period (an ordinary annuity) and the start (an annuity due).

What if I started later? is the field worth playing with. Set it to zero to skip the comparison; leave it in to see the most surprising number on the page.

Step-by-Step Example

£10,000 today, £300 a month, 7%, 30 years, compounded monthly.

  r = 7% / 12 = 0.583% per period
  n = 360 periods

  From the lump:            10,000 × (1.00583)³⁶⁰  =   81,164.97
  From the contributions:                              365,991.30
                                                     ───────────
  Future value:                                        447,156.27

  You paid in:                                         118,000.00
  Growth:                                              329,156.27

Worth pausing on the split. The £10,000 lump grew eightfold. The £300 a month — £108,000 in total — produced £365,991. Over a long horizon the contributions usually do more than the starting amount, which is the opposite of most people's intuition about where wealth comes from.

The Cost of Waiting

Same plan, started five years later:

  Full 30 years:              447,156.27
  Starting 5 years later:     300,275.69
                              ──────────
  Difference:                 146,880.58

  Contributions skipped:       18,000.00

£146,880 of final value, to avoid paying in £18,000. More than eight times the money.

The reason is that the early periods are the ones doing the most compounding — not because they are special, but because everything after them multiplies. A pound invested in year one is multiplied by thirty years of growth. A pound invested in year twenty-five is multiplied by five.

Delaying does not remove average years. It removes the most valuable ones.

The consequence people find hardest to believe

This is why someone who invests for ten years and then stops entirely often ends ahead of someone who starts ten years later and never stops — despite paying in far less. The first person's money has the extra decade of multiplication, and no amount of later contribution buys that back.

If you take one thing from this calculator, take that.

Start or End of the Period?

Paying at the start of each period buys one extra period of growth on every contribution. The effect is exactly a factor of (1 + r) on the annuity portion:

  Paid at the end of each month:    447,156.27
  Paid at the start:                449,291.22
                                    ──────────
  Worth:                              2,134.95

Small relative to the total. But it is free, it requires changing nothing except the date on a standing order, and it compounds like everything else.

Doubling Time and the Rule of 72

The rule of 72 says money doubles in 72 ÷ rate years. It is a good shortcut and an approximation that degrades away from about 8%.

The exact answer:

  t = ln 2 / ln(1 + r)

Close at 7% and 8%, where it is calibrated. Noticeably off at both ends, and in opposite directions — it under-estimates at low rates and over-estimates at high ones. The calculator gives both.

When the Rate Is Negative

The formula does not object to a negative rate, and the result is meaningful: it is what a balance becomes when it shrinks by a fixed proportion each period. That is the right model for a real return during a period when inflation runs above the nominal rate, and for an asset that depreciates steadily.

Two things behave differently there. Nothing doubles, so the doubling time is omitted rather than reported as a negative number of years. And contributions still accumulate faster than the balance erodes for a long while, which is why a plan can keep growing in cash terms while losing ground in real ones.

Which Frequency Should You Use?

Match it to when the money actually moves. A salary-funded savings plan is monthly. A bond coupon is usually twice a year. A fixed-term deposit quoting an annual rate is annual.

Getting this wrong matters less than people expect. On the example figures, switching the lump between annual and daily compounding changes the result by under 2% of the total. The rate, the term and the timing of the contributions all matter considerably more than the frequency does — a point the APY calculator makes in detail on the savings side.

Understanding Your Result

Future value is the total at the end, in the money of that time.

Yours against growth splits it between contributions and return.

Where it came from separates the lump from the payments, which is where the "contributions matter more than you think" point becomes visible.

The cost of waiting is the delay comparison — the number most likely to change what you do.

Worth knowing names the ratio between what a delay costs and what it saves.

When Should You Use This Calculator?

When deciding whether to start now or later. This is the main event.

To value a stream of payments. A pension contribution, a savings plan, a series of fixed receipts.

To check a projection. Any future-value figure you are shown should be reproducible from the rate, the amount and the period.

To understand a doubling claim. "Doubles your money in X years" implies a rate, and this recovers it.

Common Mistakes

Thinking a delay only costs the missed contributions. It costs those plus all the compounding they would have done — eight times as much here.

Mixing the rate and the period. An annual rate with monthly compounding needs dividing by twelve first, which the calculator shows explicitly.

Treating the rule of 72 as exact. It is a shortcut calibrated near 8%.

Reading the future value as spending power. It is nominal. The savings calculator converts it to today's money and takes tax off the rate.

Ignoring charges. On an investment they come off the rate every year — the investment calculator shows what that does.

Assuming a constant rate. The formula needs one; reality does not supply one. The result is a projection, not a forecast.

Every figure here is an estimate for planning, not financial advice.