Your investment,
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Field guide

How investment growth is actually calculated.

An investment with a starting principal, a fixed monthly contribution, and a constant rate of return obeys a single equation in five variables. Lock down any four of them and the fifth is determined. That's the time-value of money, and it's the engine behind every long-term planning question worth asking.

The master equation

The future value FV of starting principal P, equal monthly contributions PMT, an annual rate r compounded monthly, over n months:

The first term is the lump sum compounding by itself; the second is the future value of an ordinary annuity (an end-of-period stream of equal payments). Add them together and you have the size of the portfolio when the clock stops.

Mode 1: Solve for future value

The default, also called “projection.” Plug P, PMT, r, n into the equation above and read off FV. This is the same shape as the compound-interest calculator, useful for asking "what will I have if I keep doing what I'm doing?"

Mode 2: Solve for required starting amount

Rearrange the master equation for P:

Useful when you have a goal ($1M in 30 years), a planned contribution, and an expected return: how big a lump sum do you need to seed the account today?

Mode 3: Solve for required monthly contribution

Rearrange for PMT:

The most actionable mode for the average saver: given a target, a starting balance, an expected return, and a time horizon, what does the monthly habit need to be?

Mode 4: Solve for required rate of return

There is no closed form for r; the calculator uses bisection on [0%, 50%]. The FV equation is monotonically increasing in r for non-negative inputs, so the search converges in 60 iterations to roughly machine precision. If even a 50% annual return can't reach the goal in the time given, the calculator surfaces “no solution” rather than an absurd number.

Mode 5: Solve for time

Set x = (1 + r/12)n. After a small rearrangement:

Edge case: when r = 0 (no compounding), time simplifies to (FV − P) ÷ PMT months. When P ≥ FV already, the answer is zero years — you're already there.

Realistic rate-of-return assumptions

The historical nominal return of the S&P 500 from 1928 to 2024 is roughly 10%. Subtract long-run inflation of about 2.5–3% and you get the commonly quoted 7% real return — the default assumption in this calculator. Other broad benchmarks:

• U.S. Treasury bills (3-mo): about 3.3% nominal historically.
• 10-year Treasuries: about 4.6% nominal historically.
• Investment-grade bonds: about 5–6% nominal historically.
• S&P 500: about 10% nominal, 7% real.
• 60/40 stock-bond portfolio: about 8% nominal, 5–6% real.

Past performance is no guarantee of future results, etc. Markets are noisy on short horizons and rough but reasonable on long ones. These numbers are directional, not promises.

Compound interest is multiplicative in time

The single most useful insight from running this calculator in different modes: time matters more than dollars. A 25-year-old contributing $200/mo from now until 65 at 7% ends with about $525,000. A 35-year-old who contributes twice as much per month ($400/mo) for 30 years instead of 40 — same end age, same rate — finishes with about $489,000. Same-on-the-month savings habit; $36,000 less because of one missing decade.

Worked example: how much to save monthly for $1M

You're 30, want $1,000,000 by 60, have $10,000 saved, expect 7% annual return. Switch to Mode 3 (Monthly):

1. n = 30 × 12 = 360 months
2. r = 7% / 12 = 0.005833
3. (1 + r)^n = 1.00583360 ≈ 8.117
4. FV of starting = $10,000 × 8.117 = $81,170
5. Required PMT = (1,000,000 − 81,170) × 0.005833 / (8.117 − 1) ≈ $753/mo

Save about $753 per month, for 30 years, at 7%, starting from $10,000 and you hit the seven-figure mark.

What this calculator doesn't model

• Sequence-of-returns risk: the order in which good and bad years happen matters at the start of withdrawal. Real-world simulations use Monte Carlo or historical bootstrapping.
• Inflation: the nominal-to-real translation lives in the Retirement Calculator. For quick mental math, subtract ~2.5% from your assumed return and you have an inflation-adjusted projection.
• Taxes: capital gains, dividends, ordinary-income on bond interest. Use the Income Tax Calculator separately, or keep contributions inside a tax-advantaged account.
• Variable contributions: assumes a flat monthly amount. If you plan to escalate contributions with raises, run multiple scenarios and chain them.

Disclaimer

This calculator is a planning tool, not investment advice. Use the projections as a directional check on whether your plan is in the right ballpark; revisit annually and adjust contributions, allocation, and time horizon as your life and the markets change.