exponentialgrowthcalculator.com

Investment Growth Calculator

Enter an initial investment, an annual return, a length of time, and an optional yearly contribution to see the projected value, total contributed, and total growth update as you type.

Investment growth calculator

Lump sum invested at time zero
%
Assumed constant annual return
Number of years the investment grows
Added once per year, enter 0 for none
Projected Value FV 68,543.01 after 20 years at 7% return
Total Contributed 29,000.00 principal + contributions
Total Growth 39,543.01 projected value − total contributed

Year-by-Year Balance

YearBalanceGrowth
0 5,000.00 N/A
1 6,550.00 1,550.00
2 8,208.50 1,658.50
3 9,983.10 1,774.60
4 11,881.91 1,898.82
5 13,913.65 2,031.73
6 16,087.60 2,173.96
7 18,413.73 2,326.13
8 20,902.69 2,488.96
9 23,565.88 2,663.19
10 26,415.49 2,849.61
11 29,464.58 3,049.08
12 32,727.10 3,262.52
13 36,218.00 3,490.90
14 39,953.26 3,735.26
15 43,949.98 3,996.73
16 48,226.48 4,276.50
17 52,802.34 4,575.85
18 57,698.50 4,896.16
19 62,937.40 5,238.90
20 68,543.01 5,605.62

What the table shows: at the default settings, a $5,000 initial investment growing at a 7% annual return for 20 years, with $1,200 added at the end of every year, the balance compounds from $5,000.00 to $68,543.01. Of that total, $29,000.00 came directly from the principal and 20 years of contributions, and $39,543.01 came purely from investment growth compounding on top of that money.

Definition

What Is Investment Growth?

Investment growth is the compound interest formula applied to a starting balance plus regular additions, so both the original money and every deposit made afterward compound together over time.

A $5,000 deposit earning a steady 7% return does not simply gain 7% of $5,000 every year. It gains 7% of whatever the balance has grown to, so the dollar amount added gets larger each year even though the percentage never changes. Layer a recurring contribution on top of that, and every deposit starts compounding from the moment it lands, just on a shorter clock than the money that arrived before it.

This is where CAGR, compound annual growth rate, comes in. CAGR is the single, constant annual return that would carry an investment from its starting value to its ending value, smoothing away every real-world up-and-down year into one flat number. The annual return entered into this calculator functions as an assumed CAGR: it describes what a smooth, unchanging rate of return would produce, which is a simplification of how markets actually behave but a mathematically well-defined quantity in its own right.

Plotted against time, an investment growing under a fixed CAGR with contributions traces a rising curve that climbs faster the longer it runs, because both the lump sum and every past deposit are being multiplied by the growth factor simultaneously. Anyone who has used the exponential growth calculator anchoring this site's homepage has already seen the shape of that curve. This page simply adds a recurring deposit into the same underlying mathematics.

Equation

The Investment Growth Formula

The investment growth formula combines a lump-sum compounding term with a recurring-contribution term: FV = P0(1 + r)t + C × [((1 + r)t − 1) / r]. The first piece grows the starting balance on its own; the second piece adds up the value built by every yearly deposit.

Lump sum, grows for the full duration
P0(1 + r)t

The starting balance compounds on its own for all t years, unaffected by whatever contributions are added along the way.

Contributions, an ordinary annuity
C × [((1 + r)t − 1) / r]

Each yearly deposit compounds only for the years remaining after it lands, the first deposit grows for nearly the whole timeframe, the last grows for none of it.

Variables in the investment growth equation
SymbolNameWhat it representsExample
FVProjected valueThe total balance after t years of growth and contributions.$68,543.01
P0Initial investmentThe lump sum invested at time zero, before any growth or deposits.$5,000
rAnnual return rateThe assumed constant annual return, as a decimal.0.07 (that is 7%)
tYearsHow many years the investment compounds.20 years
CAnnual contributionThe amount added once per year, at the end of the year.$1,200/year

What the table shows: five symbols cover the whole formula, and only P0, r, t, and C are ever typed in by hand. FV is the computed result. The contribution term divides by r, so when the annual return is exactly 0% the calculator switches to C × t instead, since dividing by zero has no defined value; with no growth at all, t years of level contributions simply add up to C times t.

Method

How to Project Investment Growth

To project investment growth, convert the annual return to a decimal, raise one plus that decimal to the power of the number of years for the lump-sum growth factor, then add the contribution term built from the same factor.

  1. Write down the initial investment

    Identify P₀, the lump sum invested before any growth or contributions.

  2. Convert the annual return to a decimal

    Divide the percentage return by 100. A 6% return becomes r = 0.06.

  3. Raise (1 + r) to the power t

    This is the lump-sum growth factor. With r = 0.06 over 15 years, (1.06)15 = 2.396558.

  4. Multiply P₀ by the growth factor, then compute the contribution term

    P₀ × (growth factor) gives the lump-sum future value; C × [(growth factor − 1) / r] gives the value built by the contributions.

  5. Add the two results together

    Combine both terms to get FV, the total projected value.

Worked example, a starter retirement account

A 22-year-old opens a retirement account with a $2,000 initial deposit, expects a 6% average annual return, and commits to adding $600 at the end of every year. The investment growth formula gives the account balance after 15 years.

P0
$2,000
r
6% → 0.06
t
15 years
C
$600/year
FV = P0(1 + r)t + C × [((1 + r)t − 1) / r] FV(15) = $2,000 × (1.06)15 + $600 × [((1.06)15 − 1) / 0.06] FV(15) = $2,000 × 2.396558 + $600 × 23.2760 FV(15) = $4,793.12 + $13,965.58 FV(15) = $18,758.70

Of that $18,758.70 balance, $11,000.00 came directly from the initial deposit plus 15 years of contributions, and $7,758.70 came from investment growth compounding on top, about 59% of the final balance is principal and contributions rather than growth, since 15 years at a 6% return has not yet reached the point where compounding dominates the outcome the way it does over longer horizons.

Limitations

Why This Is a Mathematical Model, Not a Guarantee

This calculator assumes a single, constant annual return for every year of the projection, which is a deliberate simplification rather than a prediction. Real investment returns swing from year to year, a portfolio might rise 18% one year and fall 12% the next, and the sequence of those swings, not any one smooth number, is what an investor actually experiences.

This calculator is a mathematical projection tool, not financial advice. It shows what a fixed rate of return would produce if it held steady for every year of the timeframe entered; it does not account for market volatility, fees, taxes, inflation, or any of the other factors that separate a real portfolio's outcome from a clean exponential curve. Real investment returns vary and are not guaranteed, and no calculator, this one included, can promise otherwise.

Underneath the two extra inputs, years and a recurring contribution, the arithmetic is identical to plain compound interest. The lump-sum portion of the formula above is exactly the equation used by the plain lump-sum calculator, and setting the contribution to zero collapses this page into that same calculation. Both, in turn, run on the same exponential engine as the exponential growth calculator at the root of this site, a starting value, a fixed rate, and elapsed time, compounding together.

Questions

Frequently Asked Questions

What does CAGR mean?

CAGR stands for compound annual growth rate, the single constant annual return that would carry an investment from its starting value to its ending value over a given number of years, smoothing out every year-to-year swing along the way. The annual return input on this calculator plays exactly that role: entering 7% assumes the balance compounds at a level, unchanging 7% every single year.

A real portfolio's CAGR is normally calculated after the fact, once the ending value is already known. This calculator runs the same relationship forward instead, using an assumed CAGR to project an ending value.

What is the investment growth formula, and what does the contribution term represent?

The investment growth formula is FV = P₀(1 + r)^t + C × [((1 + r)^t − 1) / r], where the first term compounds the starting balance alone and the second term adds the value built up by regular contributions. The contribution term is the future value of an ordinary annuity. It accounts for the fact that each deposit compounds for a different length of time, since the first contribution has almost the whole timeframe left to grow and the last has none.

When the annual return is exactly 0%, that division by r is undefined, so the contribution term simplifies to C × t: just the deposits added up, with no growth on top.

How does a constant assumed return differ from real investment returns?

A constant assumed return smooths every year into one identical number, while real investment returns vary from year to year and can be negative in any given year. Two portfolios that average the same return over ten years can end at noticeably different balances depending on the order the good and bad years arrive in, a detail a constant-rate projection cannot capture.

This tool performs a mathematical projection only. It is not financial advice, and no fixed-rate calculation can guarantee what a real investment will actually return.

Why does starting earlier matter more than contributing more later?

Starting earlier matters more than contributing more later because elapsed time compounds exponentially through the (1 + r)^t term, while a larger contribution only adds value linearly through C. Stretching the default $5,000-plus-$1,200/year plan from 20 years to 30 years, with nothing else changed, grows the projected value from $68,543.01 to $151,414.22, even though only $12,000 more gets contributed out of pocket over that time.

Doubling the contribution instead, to $2,400/year, but keeping the same 20-year window, only reaches $117,737.60, a smaller ending balance built from $53,000 of total contributions, more money paid in for a worse result than the extra decade produced.

Is the annual contribution added at the start or the end of each year?

The annual contribution in this calculator is added once at the end of each year, after that year's growth has already been applied. This is the standard "ordinary annuity" timing used in most compound-interest formulas, and it means the very last contribution never has any time left to grow before the projection ends.

Contributing at the start of each year instead, an "annuity due", would let every deposit earn one extra year of growth, producing a slightly higher final value for the same inputs.

Can the annual return be negative?

Yes. Entering a negative annual return models a scenario where the investment loses value every year instead of gaining it, using the exact same formula with r simply below zero. A steady −4% return, for example, shrinks both the lump sum and the value of past contributions year after year rather than growing them.

The one input the calculator rejects is a return at or below −100%, since that would imply the entire balance disappearing or going negative in a single year, which the underlying formula has no meaningful way to represent.

Does this calculator account for taxes, fees, or inflation?

No. This calculator does not account for taxes, fees, or inflation; it projects raw growth under a single assumed annual return only. Any of those factors would reduce the real-world spending power of the projected value shown here, sometimes substantially over a long time horizon.

Treat the output as a clean mathematical projection of compounding, not a net, after-cost, or inflation-adjusted figure.

How is an investment growth calculator different from a compound interest calculator?

This calculator differs from a plain compound interest calculator only by adding a recurring annual contribution on top of the same lump-sum compounding math. Setting the contribution to $0 here reproduces exactly the same result as the compound interest calculator, since the annuity term then contributes nothing.

Everything else, the growth factor, the assumed constant rate, the exponential shape of the curve, is identical between the two tools.