What this calculator does
Find out how much your investments could grow to, or what it would take to reach a goal. Every investment plan has the same five parts. There's what you start with, what you add regularly, and the return you earn. Then there's how long you stay invested, and where you end up. If you know any four, the fifth is set. So you choose which one to solve for. That answers the questions people really ask: How much will I have? How much should I invest each month? What return would it take? How long will it take?
Pick what to solve for and enter the other values. The calculator shows the answer and how it got there. It also shows the total you put in and how much came from growth. If you like, it shows the result in today's dollars too. A table and chart show your balance year by year. It works for any long-term investment you can describe with an average yearly return. That includes a brokerage account, an index fund or an IRA.
Where it's used
Why this math matters outside the classroom:
- Projecting a balance. Starting with $10,000 and adding $300 a month at an assumed 7% a year shows how the balance could grow over 20 years.
- Required contribution. Savers solve for the monthly amount needed to reach a set balance by a set year at an assumed return.
- Required return. Working backward finds the yearly return that would turn a given plan into a target balance.
- Time to a goal. Logarithms give the number of years needed for deposits and growth to reach a target amount.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose what to solve for: end balance, contribution, return rate or years.
- Enter your starting amount. Depending on what you're solving for, also enter the regular contribution, the average yearly return, the number of years and your target balance.
- Choose whether you add money monthly or yearly, and whether it goes in at the start or end of each period. You can also enter inflation if you like.
- Read the answer and the steps behind it. Then check the yearly table to see how your balance builds, and when growth starts adding more than you do.
What the inputs mean
- Solve for
- The value you want the calculator to find. The box for that value is hidden, because it becomes the answer.
- Target end balance
- The balance you want to reach. It's used when solving for the contribution, the return or the years.
- Contribute every
- How often you add money. The yearly return is turned into a matching monthly rate, so a full year always grows by exactly the yearly figure.
- Contributions are made at the
- Money added at the start of a period is invested for that whole period. So it ends slightly higher than the same money added at the end.
- Average annual return
- An average yearly return after fund fees. For example, 6% or 7% for a broad mix of mostly stocks over long periods. This is a guess, not a forecast. Real returns change a lot from year to year, and some years they're negative.
- Inflation
- Optional. The calculator divides the end balance by how much prices rise over the same years. That shows what the money would buy in today's dollars.
Formula and method
rate per period: i = (1 + r)^(1 ÷ p) − 1 end balance: FV = P × (1 + i)^n + C × ((1 + i)^n − 1) ÷ i start-of-period contributions: multiply the C term by (1 + i) contribution: C = (target − P × (1 + i)^n) ÷ (((1 + i)^n − 1) ÷ i) periods: n = ln((target + A) ÷ (P + A)) ÷ ln(1 + i), where A = C ÷ i return: the r for which FV equals the target, found by bisection
In the formulas, P is your starting amount and C is what you add each period. r is the yearly return as a decimal, so 7% is 0.07. p is how many times a year you add money (12 or 1), and i is the growth rate per period. n is the number of periods, and FV is the end balance (its future value). A is a helper amount, explained below, and ln is the natural logarithm, a button on most scientific calculators.
The end-balance formula has two parts. The first grows your starting amount. The second adds up every contribution, each with the growth it has earned by the end.
Solving for the contribution and for the time both have exact formulas. When solving for years, n is rounded up to the first whole month (or year) that ends at or above the target. So the answer is a point you can check in the table.
No formula can pull out the return on its own, so the calculator searches for it. It tries a rate and checks whether the end balance is too high or too low. Then it cuts the search range in half and tries again, a method called bisection. It repeats until the rate is pinned down far past the decimals shown. This always works, because a higher return always means a higher end balance.
Worked example
You have $10,000 invested and add $500 at the end of every month for 25 years, assuming a 7% average annual return.
- Monthly rate: 1.07^(1/12) − 1 ≈ 0.00565415.
- Starting amount: $10,000 × 1.00565415^300 ≈ $54,274.33.
- Contributions: 300 × $500 grow to about $391,520.94.
- End balance: $54,274.33 + $391,520.94 = $445,795.27, from $160,000 invested.
- Solving for other things with a $500,000 target: you'd need about $569.22 a month, or a 7.72% average return at $500 a month, or 318 months (26.5 years) at 7% and $500 a month.
Result: The end balance comes to about $445,795.27. Of that, $285,795.27 is investment growth.
Understanding the result
Over long periods, growth usually ends up adding more than you put in yourself. In the example, growth makes up nearly two thirds of the end balance. That's why time invested matters so much. A few extra years can change the answer more than a bigger contribution.
Sometimes the return you'd need is well above what your mix of investments has earned over long periods. Treat that as a warning sign. The plan probably needs a bigger contribution, more time or a smaller target, rather than riskier investments. Solving the same goal for different things shows which change is most realistic for you.
Assumptions and limitations
- You earn the same average return every year. For monthly contributions, it's turned into a matching monthly rate.
- You add the same amount every period and never skip one. Nothing is taken out.
- Fund fees are already counted in the return you enter. Taxes on dividends, gains or withdrawals aren't included.
- Real markets don't grow at a steady rate. The order of good and bad years matters, especially near the end of a plan. A steady-rate estimate can't show that risk.
- The result is an estimate for learning and planning. It isn't investment advice or a promise of future returns.
- It doesn't handle contributions that change, lump sums added partway through, or the rules and limits of specific accounts.
Frequently asked questions
What rate of return should I use?
Use a cautious long-term average for your actual mix of investments, after fees. Over long periods, mostly-stock mixes have earned more on average than mostly-bond or cash ones, but with far bigger ups and downs. Try the plan at a low, middle and high rate. That gives you a range, instead of one number you might trust too much.
How is this different from the compound interest calculator?
The compound interest calculator grows a balance at a fixed interest rate, added a set number of times a year. This calculator is built around investing goals. It can work backward from a target to the contribution, return or time you need. And it treats the return as an average yearly growth rate.
Should I invest monthly or once a year?
For the same yearly total, money invested earlier has longer to grow. So monthly contributions usually end a little ahead of one deposit at the end of the year. A deposit at the start of the year ends ahead of both. But the difference is small next to how much you invest and for how long.
Why does the years answer go past my target?
The calculator rounds up to the first whole month (or year) that ends at or above the target. So the balance at that point is usually a little above it. The steps also show the exact number of periods from the formula, including any fraction.
Does this include taxes?
No. In a regular taxable account, dividends and gains you cash in may be taxed along the way, which lowers your real return. In accounts like a 401(k) or an IRA, taxes are put off until later. For qualified Roth withdrawals, they're avoided. To roughly allow for taxes, enter an after-tax return.
How this calculator is checked
Method: Future value of a lump sum plus an ordinary annuity or annuity due at the effective periodic rate; algebraic inversions for the payment and (via logarithms) the number of periods; bisection for the rate. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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