Lump Sum Investment Calculator
Investing a single amount and leaving it alone is the simplest case in finance, and the one where the arithmetic is least forgiving: with no further contributions, every dollar of the result comes from the rate and the time.
Growth Is Exponential, and That Is Counter-Intuitive
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final = principal × (1 + rate)^years
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| $100,000 at 7% | Value | Gain that decade |
|---|---|---|
| 10 years | $196,715 | $96,715 |
| 20 years | $386,968 | $190,253 |
| 30 years | $761,226 | $374,258 |
| 40 years | $1,497,446 | $736,220 |
The fourth decade adds more than the first three combined. This is why the single most
important variable in a lump-sum projection is not the rate — it is how long you leave it
alone.Lump Sum Usually Beats Averaging In
Historically, investing a windfall immediately has outperformed spreading it over months
roughly two-thirds of the time, for the plain reason that markets rise more often than they
fall — time out of the market is the cost.
The argument for spreading it is behavioural, not mathematical: a 30% drawdown one month
after investing everything is what makes people sell at the bottom. If phasing in over three
to six months is the difference between staying invested and panicking, it is worth the
expected cost.
Sequence Risk Cuts Both Ways
A lump sum has no averaging effect, so the entry point matters more than for a regular
contributor. That is uncomfortable but not a reason to wait — nobody has reliably identified
the entry point in advance, and cash held while waiting has a guaranteed real loss to
inflation.
Real Returns, Not Nominal
A 7% nominal return with 3% inflation is about 3.9% real, not 4% — the correct calculation
divides rather than subtracts. Over 30 years that $761,226 has the purchasing power of
roughly $313,000 in today's money. Project in real terms or you will badly overestimate what
the number buys.
Where It Sits Matters
Held in a taxable account, dividends and realised gains are taxed along the way, which drags
the effective rate. The same lump sum in a tax-advantaged account compounds untouched. Fill
the tax-advantaged space first.
The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
| Year | Deposited | Balance | Growth | Growth on deposits |
|---|---|---|---|---|
| 1 | $12,400 | $13,201 | $801 | 6% |
| 5 | $22,000 | $28,495 | $6,495 | 30% |
| 10 | $34,000 | $54,714 | $20,714 | 61% |
| 20 | $58,000 | $144,573 | $86,573 | 149% |
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
`
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
``
The second term usually dominates. On these numbers the $200 monthly contribution accounts for the larger share of the final balance, which is the practical lesson: how much you add matters more than the rate, right up until the balance gets large.