Compound Interest Calculator with Monthly Deposits

The compound interest formula

For a single deposit, A = P(1 + r/n)^(nt), where P is the starting amount, r is the annual rate as a decimal, n is how many times per year interest compounds, and t is years. $10,000 at 7 percent compounded once a year for 30 years grows to $10,000 × 1.07^30 = $76,123.

Compound monthly instead (n = 12) and the same deposit reaches $81,165. More frequent compounding helps, but the effect is small compared with the rate and the time.

Worked example with monthly contributions

Start with $10,000, add $250 every month, earn 7 percent a year compounded monthly, for 10 years. This calculator adds each deposit at the start of the month and then applies one month of interest. After 120 months the balance is $63,620. You contributed $40,000; the other $23,620 is growth.

Stretch the same plan to 30 years and growth overtakes contributions by a wide margin. That is the whole point: in the early years, your deposits do the work; in the later years, the interest does.

The Rule of 72

Divide 72 by the annual rate to estimate how many years it takes money to double. At 7 percent: about 10.3 years. At 4 percent: 18 years. At 10 percent: 7.2 years. It works in reverse for costs too: at 3 percent inflation, prices double in roughly 24 years.

Doubling is why starting early matters more than starting big. Money invested at 25 has about four doublings at 7 percent before 65. Money invested at 45 gets two.

Realistic rates to plug in

High-yield savings accounts and money market funds pay variable rates that move with the Federal Reserve. Certificates of deposit lock a rate for a set term. The US stock market has historically returned around 10 percent a year before inflation over long periods, or roughly 6 to 7 percent after inflation, with large swings along the way.

Using 6 or 7 percent for long-term stock projections gives a result in today's dollars, which is easier to reason about. Using 10 percent gives a nominal number that will look bigger but buy less.

Starting early versus contributing more

Consider two savers earning 7 percent a year. The first invests $5,000 a year from age 25 to 35, then stops: $50,000 in total. The second starts at 35 and invests $5,000 every year until 65: $150,000 in total. At 65, the early saver has about $563,000 and the late saver about $505,000. A third of the money, ten extra years to compound, and she still comes out ahead. Time is the input you cannot buy back.

That does not mean late starters should give up. It means the lever shifts from time to contribution size. Someone starting at 40 can still build a substantial balance by capturing the full employer 401(k) match, using catch-up contributions after 50, and keeping fees low.

APR versus APY

APR is the simple annual rate. APY includes the effect of compounding within the year. A 5 percent APR compounded monthly is an APY of about 5.12 percent. Banks advertise APY on savings because it is the bigger number, and APR on loans because it is the smaller one. When comparing savings accounts, compare APY to APY.

For loans, compounding works against you. Credit card interest compounds daily on most US cards, so a 24 percent APR carries an effective annual rate above 27 percent if you never pay it down.

What eats compound growth

Fees compound too. A 1 percent annual fee on a portfolio earning 7 percent cuts the effective return to 6 percent. Over 30 years on $10,000, that is the difference between $76,123 and $57,435, about a quarter of the final balance.

Taxes matter as well. Tax-advantaged accounts like a 401(k), IRA, or Roth IRA let growth compound without annual tax drag. This tool shows gross growth and runs entirely in your browser; treat it as a planning estimate, not a guarantee of returns.