What this calculator does
See how much a stock or fund could grow when you use every dividend to buy more shares. A dividend is a cash payment a company or fund makes to its shareholders. You can take the cash, or use it to buy more shares. If you reinvest, the next dividend is paid on a few more shares. So the payouts compound (grow on top of earlier growth), on top of any rise in the share price. Over a decade or two, that quiet compounding can make up a large part of an investment's total growth.
The calculator shows both paths side by side. Enter what you invest, the share price and the dividend yield. Then add how fast you expect the price to grow and how often dividends are paid. You get the ending value with dividends reinvested and the number of shares you'd own. You also see the dividends you'd receive in the final year, and how much more reinvesting earns than spending the dividends. An optional tax rate shows the effect of paying tax on each dividend in an ordinary taxable account.
Where it's used
Why this math matters outside the classroom:
- Long-term investing. An investor holding 200 shares that pay 0.75% of the price each quarter sees the share count reach 200 × 1.0075^80, about 364, in 20 years.
- Retirement income planning. Savers estimate the yearly dividend income their shares would pay at retirement if dividends are reinvested until then.
- Algebra 2 lessons. Students model a share count that grows by a constant percent each period and compare it with a fixed count plus cash.
- Comparing account types. Investors compare reinvesting in a taxable account with a tax-free one by entering a dividend tax rate.
- Personal finance clubs. Members compare a 2% yield with 7% price growth against a 5% yield with 2% growth over 15 years.
Grade level and standards: Grades 10–12; Common Core State Standards for Mathematics HSF.LE.A.1.c, HSF.LE.A.2, HSA.SSE.B.3.c. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the amount you invest today and the current share price.
- Enter the dividend yield and your guess for yearly share price growth.
- Choose the number of years and how often dividends are paid. Add a tax rate if the dividends will be taxed each year.
- Read the ending value and share count. Then use the table and chart to compare reinvesting with taking cash.
What the inputs mean
- Dividend yield per year
- The yearly dividend divided by the share price. The calculator keeps this percent fixed, so as the price rises, each dividend payment rises with it. A stock whose dividend grows faster or slower than its price will do better or worse than shown.
- Share price growth per year
- A guess, not a forecast. Over the long run, share prices for broad markets have risen on average. But they vary a lot from year to year, and single stocks can fall. Try several values.
- Dividends are paid
- How many dividend payments there are each year. The yearly yield is split evenly across the payments. More frequent payments compound slightly faster, because each one starts earning sooner.
- Tax on dividends (optional)
- Taken from every payment before the rest is reinvested. Leave it blank for a tax-advantaged account, where dividends aren't taxed as they're paid.
Formula and method
starting shares = investment ÷ share price shares after n payments = starting shares × (1 + y × (1 − tax) ÷ p)^n share price after t years = price × (1 + g)^t value with reinvestment = shares × final price value taking cash = starting shares × final price + all cash dividends
In the formulas, y is the yearly dividend yield and p is the number of payments a year. g is the yearly price growth, t is the number of years, and n = p × years is the number of payments. Each payment is a fixed share of the share price. So reinvesting it at that same price always adds the same share to your share count: y ÷ p of it, less tax. That's why the share count grows like a savings balance at a steady rate.
The value is the share count times the share price. So total growth is the two growth factors multiplied together. Turned into a yearly rate, that gives the total return per year: (1 + g) × (1 + y(1 − tax) ÷ p)^p − 1. Without reinvesting, the share count stays the same and the dividends pile up as cash. The calculator assumes that cash earns nothing.
Worked example
You invest $10,000 in shares priced at $50 with a 3% yield paid quarterly. You assume the price grows 5% a year and hold for 20 years in a tax-free account.
- Starting shares: $10,000 ÷ $50 = 200.
- Each quarterly dividend is 3% ÷ 4 = 0.75% of the share price, so reinvesting it multiplies the share count by 1.0075.
- After 80 payments: 200 × 1.0075^80 = 363.6088 shares.
- Share price after 20 years: $50 × 1.05^20 = $132.66.
- Value: 363.6088 × $132.66 = $48,238.12.
- Taking the dividends as cash instead leaves 200 shares worth $26,532.98 plus $10,227.89 in dividends, a total of $36,760.87.
Result: With dividends reinvested, the $10,000 grows to $48,238.12 and pays $1,394.95 in dividends in the final year. That's $11,477.25 more than taking the dividends as cash.
Understanding the result
The gap between the two lines on the chart is the payoff from compounding the dividends. It starts small and widens every year. That's because each reinvested dividend buys shares that pay their own dividends later.
The final-year dividend figure is a handy income check. If you plan to live on dividends one day, it shows the yearly cash the shares would pay once you stop reinvesting, if the yield holds.
The total return per year combines price growth and the reinvested yield. In the example it's about 8.19%. That's a little more than 5% plus 3%, because the quarterly reinvesting compounds within each year.
Assumptions and limitations
- The share price grows smoothly at the same rate every year, and the dividend yield stays the same.
- Dividends are paid at the end of each period and reinvested right away at that day's price. They buy partial shares, with no fees.
- Cash dividends that aren't reinvested earn no interest, and no new money is added.
- Real prices and dividends rise and fall in ways no one can predict. Companies can cut or stop dividends. Treat the projection as a picture of how compounding works, not a prediction.
- Tax is modeled as one flat rate on each dividend. Real tax depends on the account, the type of dividend and your situation. Selling shares later may also bring more tax.
- Inflation isn't taken out. Use the real rate of return calculator to turn the result into today's dollars.
Frequently asked questions
Does reinvesting dividends really make a big difference?
Over short periods the difference is modest. Over long ones it can be large. In the example, reinvesting 3% a year adds about 31% to the ending value after 20 years. The longer you hold and the higher the yield, the bigger the gap.
Do I pay tax on dividends I reinvest?
In an ordinary taxable account, generally yes. A reinvested dividend is usually treated as if you got the cash and then bought shares. Tax-advantaged retirement accounts typically don't tax dividends as they're paid. Check the rules for your own account.
Why does the calculator keep the yield constant instead of the dividend?
Keeping the yield constant means dividends grow at the same rate as the share price. That's a neutral, simple assumption. If you expect the dividend to stay flat while the price rises, the real result would be lower. If you expect dividends to grow faster than the price, it would be higher.
Is a higher dividend yield always better?
Not on its own. A high yield can come from a falling share price, or a payout the company may not keep up. What matters for growth is the total return: dividends plus price change. A stock with a modest yield and strong price growth can outgrow a high-yield stock with a flat price.
How this calculator is checked
Method: Period-by-period simulation of fractional-share reinvestment at a constant dividend yield and smoothly compounding share price; it equals the closed form shares₀ × (1 + y(1 − t)/p)^n × P₀(1 + g)^years, which the tests check independently. 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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