Compound interest calculator: how a balance and deposits grow

A compound interest calculator answers a question with two moving parts: what does money already invested grow into, and what does a stream of regular contributions add on top of it?

Those are separate calculations with separate formulas. A starting balance grows geometrically and needs nothing further from you. A monthly contribution builds a series in which each deposit compounds for a different length of time -- the first one for the whole period, the last one for a single month. Adding them gives the ending balance.

The return you enter is an assumption, not a forecast. Real portfolios do not deliver the same percentage every year, and some years are negative. Everything below is arithmetic about a chosen rate, which is useful precisely because it isolates what the rate, the term and the deposit each contribute.

#Two formulas, then one

The starting balance follows the standard compound growth equation:

Formula: FV = PV * (1 + i)^N where PV is the starting balance, i is the rate per compounding period (annual rate / periods per year), and N is the total number of periods (years x periods per year).

The contributions follow the future value of an ordinary annuity, which assumes each deposit lands at the end of its period:

Formula: FV = C * ((1 + i)^N - 1) / i where C is the contribution per period. The bracketed term is the sum of a geometric series: one deposit compounds for N-1 periods, the next for N-2, and so on down to the last, which earns nothing.

The calculator runs both and adds them:

Formula: Ending balance = PV * (1 + i)^N + C * ((1 + i)^N - 1) / i

When the compounding frequency is not monthly, the calculator converts the monthly contribution into the equivalent amount per compounding period -- annual compounding means one deposit of twelve months' contributions at the end of each year.

#A worked example, done by hand

Take $1,000 starting, $250 a month, an assumed 6% annual return, 25 years, compounded monthly.

1. Rate per period: 0.06 / 12 = 0.005. Periods: 25 x 12 = 300.
2. Growth factor: (1.005)^300 = 4.46496981.
3. Starting balance grows to: 1,000 x 4.46496981 = $4,464.97.
4. Annuity factor: (4.46496981 - 1) / 0.005 = 3.46496981 / 0.005 = 692.993962.
5. Contributions grow to: 250 x 692.993962 = $173,248.49.
6. Ending balance: 4,464.97 + 173,248.49 = $177,713.46.

Worked example: You put in 1,000 + (250 x 12 x 25) = $76,000. The balance is $177,713.46, so growth is $101,713.46, which is 57.2% of the final balance. The $1,000 starting balance accounts for only $3,464.97 of the growth; the rest comes from the deposits.

#Nominal rate versus effective annual yield

The rate you type is a nominal annual rate. It is divided into periods and applied period by period, so the amount actually earned over a year is slightly higher than the nominal figure.

Formula: APY = (1 + nominal rate / f)^f - 1, where f is compounding periods per year.

At 6% compounded monthly: (1 + 0.005)^12 - 1 = 0.0616778, an effective 6.1678% a year. That is the figure the calculator reports as the effective annual yield, and it is the number that makes two accounts with different compounding schedules comparable. Deposit accounts are typically advertised as an APY for exactly that reason.

#What changing the compounding frequency actually does

Less than most people expect. The table isolates the effect using a single $10,000 lump at an assumed 5%, held ten years with no contributions.

Going from annual to daily compounding over a decade adds about 1.2% to the ending balance. The jump from annual to monthly captures most of it; everything beyond monthly is rounding by comparison. The rate itself, and the number of years, matter enormously more.

The same run with the calculator's default inputs -- $1,000 start, $250 a month, an assumed 6%, 25 years -- gives $168,885.41 annually, $176,034.33 quarterly, $177,713.46 monthly and $178,537.97 daily. Note that part of that spread is contribution timing, not compounding: at annual frequency, twelve months of deposits sit and wait until the end of the year before they start earning.

#Doubling time, and how far to trust the rule of 72

Divide 72 by the rate written as a percentage and the answer is roughly the number of years a balance needs to double. As mental arithmetic it is remarkably good, and around 8% it is very nearly exact.

The exact figure is ln(2) / ln(1 + rate). The approximation drifts at both ends: it is a year too slow at 2% and a fifth of a year too fast at 20%. The calculator reports the exact doubling time using the effective yield, so at 6% compounded monthly it shows 11.58 years rather than 12 -- the compounding raises the effective rate to 6.1678%, which doubles slightly faster.

#Why time matters more than the size of the contribution

Both raise the ending balance, but only one of them compounds. Contributing twice as much for half as long puts identical money in and produces a very different result.

The difference is $266,852.23 on the same cash, because the early deposits have decades of compounding behind them. The same effect appears in the growth share over time, using the default inputs:

Growth passes contributions somewhere between years 20 and 25 at this rate. Before that, the balance is mostly your own money; after it, mostly compounding.

#Where each input comes from

Starting balance. What is invested today in the account you are modeling. Keep separate accounts in separate runs if their assumptions differ.

Monthly contribution. The amount you actually add. For tax-advantaged accounts, the 2026 elective deferral limit for 401(k)-type plans is $24,500, with an $8,000 catch-up at 50 and over and $11,250 at ages 60 to 63; the IRA limit is $7,500 with a $1,100 catch-up. Employer contributions are additional and can be entered here as part of the monthly figure.

Assumed annual return. This is the input the answer is most sensitive to, and the one nobody can know. Running the page at several rates -- a pessimistic, a central and an optimistic figure -- is more informative than a single number.

Years. The second most important input, and often the most controllable.

Compounding frequency. Match the account: deposit accounts commonly compound daily or monthly, while a broad market fund has no compounding schedule at all and monthly is a reasonable modeling choice.

#How to read the result

The ending balance is a projection under one fixed assumption, not a prediction. Its most useful property is comparison: the same run at 5% and at 7% brackets a plausible range, and the gap between those two numbers is the honest measure of uncertainty.

The growth share tells you how much of the balance came from compounding rather than from deposits, which is a direct measure of how much time has done. A 25-year run at 6% is 57.2% growth; a 5-year run is 14.9%.

The ending balance is in nominal dollars. To see what it buys, run it through the inflation calculator, or use the savings goal calculator to work backwards from a target instead.

#What this model leaves out

• Volatility. A real portfolio does not return the same percentage every year. Two portfolios averaging the same return can end at different values depending on the order of the returns, because a loss early on removes capital that would have compounded.
• Taxes. Interest, dividends and realized gains may be taxable outside a tax-advantaged account.
• Fees. Expense ratios and advisory fees come out of the return, so a 6% gross return may be a lower net figure.
• Inflation. All figures are nominal. A given balance buys less at the end than the same balance would today.
• Contribution timing. Deposits are treated as landing at the end of each period. Depositing at the start of each period multiplies the annuity portion by (1 + i), a small increase.
• Contribution changes. The monthly amount is constant; in practice, contributions often rise with income.
• Withdrawals. Nothing is taken out during the period.

#Common mistakes

Reading the ending balance as an expectation. It is arithmetic on an assumption. The output is only as good as the rate typed in.

Chasing compounding frequency. As the table shows, moving from annual to daily compounding at 5% adds roughly 1.2% over ten years. The rate and the horizon dominate.

Confusing nominal rate with APY. Comparing a nominal rate against another account's APY overstates one of them. Convert both to APY first.

Forgetting inflation when the horizon is long. A 40-year projection in today's dollars is a different number from the same projection in nominal dollars.

Assuming a smooth path. The curve on the page is the average outcome of a constant rate; a real balance wanders around it, sometimes far below. The credit card payoff calculator shows the same mathematics running against you, and the full calculator index covers the rest of the picture.