Savings & Investment Calculator

Last updated: 2026-05-05

Savings growth and compound interest

Savings growth is the increase in an account balance over time from two sources: the money paid in (an initial deposit plus recurring contributions) and the interest earned on the accumulated balance. When interest is added back to the principal so that future interest is calculated on the larger sum, the growth is compound rather than simple. The final balance depends on three quantities: the amount contributed, the length of time the money compounds, and the rate of return.

This calculator computes the final balance from those three inputs, plots the year-by-year growth curve, and optionally deflates the final figure by an assumed inflation rate to express it in today's purchasing power.

Why compounding accelerates

Each period's interest is added to the principal, and the next period's interest is calculated on that larger base. Early on, the balance is close to the amount contributed, so interest is a small share of the total. As the balance grows, the interest earned each year grows with it, and the gap between total contributions and total balance widens.

A comparison with simple interest makes the effect concrete. Take $10,000 at 5% per year:

The gap accelerates with time, which is why elapsed time affects the outcome more than the contribution amount. A person contributing $200/month from age 25 to 65 typically ends with more than someone contributing $600/month from 45 to 65, even though the late starter pays in three times as much.

Formula

The final value is the future value of the initial deposit plus the future value of the stream of monthly contributions:

$FV = P_0 \cdot \left(1 + \frac{r}{12}\right)^{12t} + C \cdot \frac{\left(1 + \frac{r}{12}\right)^{12t} - 1}{\frac{r}{12}}$

where $P_0$ is the initial deposit, $C$ is the monthly contribution, $r$ is the annual return, and $t$ is the number of years. The growth curve in the chart evaluates the same formula at every year $\tau$ in the range $0 \le \tau \le t$, so the year slider shows the projected balance, cumulative contributions, and cumulative interest at each point — including the crossover where interest begins to exceed contributions.

Goal-seek mode inverts the formula to solve for the monthly contribution $C$ that reaches a target balance:

$C = \frac{\left(\text{goal} - P_0 \cdot (1 + r/12)^{12t}\right) \cdot (r/12)}{(1 + r/12)^{12t} - 1}$

Worked example

A starting balance of $0 with a $100/month contribution at a 7% annual return reaches a balance after 18–20 years where cumulative interest first exceeds cumulative contributions. For roughly the first two decades the contributions dominate the balance; after the crossover, interest is the larger component. On the growth curve, this is the point where the dotted interest line rises above the dashed contribution line.

Reading the growth curve

The chart plots three curves against time:

• Balance (solid green) — the total balance at year $\tau$, which curves upward as compounding accelerates.
• Cumulative contributions (dashed blue) — the amount paid in by year $\tau$, which grows linearly.
• Cumulative interest (dotted orange) — the difference between the two, near zero in the early years and steepening later.

The point where the interest curve crosses above the contributions curve marks the inflection where compounding becomes the larger source of growth.

Nominal and real balances

A 7% nominal return at 3% inflation corresponds to a real return of roughly 4%. The inflation adjustment section sets an expected annual inflation rate, and the calculator divides the final nominal balance by $(1 + i)^t$ to give the real balance — what the future amount buys in today's money.

For example, at 2% inflation over 30 years, $1 today is worth about $0.55 in 2055, so a $500,000 balance at year 30 has the purchasing power of about $275,000 today. The nominal figure measures the account balance; the real figure measures what it can buy.

Forecast and goal-seek modes

The mode selector at the top of the calculator switches between two questions:

• Forecast (default) — the contribution is set and the calculator returns the final balance, answering "how much will the account hold?"
• Goal-seek — a target balance is set and the calculator inverts the formula to return the required monthly contribution, answering "how much must be saved each month?"

If the initial deposit alone, compounded at $r$ over $t$ years, already meets the goal, the required contribution clamps to 0 and the calculator notes that no further saving is needed. Both modes share the same growth-curve chart and inflation adjustment.

Applications

Estimating a retirement contribution

For a target of $1 million by age 65, starting at 30 with nothing at a 7% nominal return, goal-seek mode returns a required contribution of roughly $820/month. Setting inflation to 2% shows the same nominal target as about $552k in today's purchasing power, so reaching that real figure requires scaling up the goal or contribution. The required contribution rises sharply the later saving begins, because there are fewer years for compounding to work.

Sizing tax-advantaged accounts

In the US, the 2024 IRA contribution limit is $7,000/year ($583/month) and the 401(k) limit is $23,000/year ($1,917/month). Entering those amounts for 30 years at 7% shows the long-run effect of contributing the maximum to tax-advantaged accounts.

Comparing nominal and real outcomes

Setting inflation to 3% over a 30-year horizon shows how far the real balance trails the headline nominal balance. Two portfolios with identical nominal returns can have different real outcomes if they span different inflation periods.

Limitations

• Taxes and fees — this is a pre-tax, pre-fee model. Tax-advantaged accounts (401k, IRA, Roth) shelter growth, while taxable brokerage accounts owe capital-gains tax. Fund expense ratios (0.03% to 1%+ per year) reduce the effective return.
• Return variance — a stated rate such as 5% is a long-run average. Actual annual returns range from about −40% to +30%, and selling during a downturn locks in losses.
• Sequence-of-returns risk — in retirement, a large drawdown in the first year of withdrawals reduces a portfolio more than the same drawdown later. A single-rate model does not capture this.
• Liquidity — the model assumes the principal is left untouched. An emergency fund of 3–6 months of expenses, held separately, is the usual precondition before long-term compounding.
• Variable inflation — the model assumes a constant inflation rate, while consumer prices move year to year and the inflation rate of a specific spending category (rent, healthcare, education) can differ from the headline figure.

Compounding produces its full effect only on money left invested over a long horizon; with frequent withdrawals, compound and simple returns converge. One condition that works against this math is high-rate debt: a typical 5–7% expected portfolio return is below a 18–22% credit-card APR, so a high-rate balance is usually cleared before investing. The Credit Card Payoff Calculator shows how long that takes — for example, $5,000 at 22% APR with $200/month clears in just under 33 months, and raising the payment to $300 saves over $1,000 in interest.