Compound Interest Calculator with Monthly Deposits

Free compound interest calculator: starting amount, monthly or yearly deposits, any interest rate and compounding, inflation and tax, with a year-by-year table and growth chart, the rule of 72, and how much to save to reach a goal.

Starting amount

Regular deposit

How often

Deposit at the

Interest rate (per year)

Compounded

Years

+ Months

More options

Raise the deposit each year by

Inflation (to show today's money)

Tax on interest

Currency

Tax is taken from the interest as it is earned (like a normal taxable savings account). Inflation does not change the balance; it shows what the money would buy in today's prices.

Growth over time

Money you put inInterest earned

Move over the chart to see any year.

Year by year

Click a year to see each month.

The formulas

one amount $ \displaystyle A = P\left(1+\frac{r}{n}\right)^{nt} $

continuous $ \displaystyle A = P\,e^{rt} $

regular deposits $ \displaystyle A = P(1+i)^{N} + D\,\frac{(1+i)^{N}-1}{i} $

yearly growth (APY) $ \displaystyle \text{APY} = \left(1+\frac{r}{n}\right)^{n}-1 $

doubling time $ \displaystyle t_2 = \frac{\ln 2}{\ln(1+\text{APY})} \approx \frac{72}{100\,r} $

P = starting amount, r = yearly rate as a decimal (5% = 0.05), n = compounding periods per year, t = years, D = deposit per period, i = growth per deposit period (with monthly compounding and monthly deposits i = r/12), N = number of deposits. Deposits at the start of each period earn one more period: multiply the deposit part by (1 + i).

How compound interest works

With simple interest you earn interest only on the money you put in. With compound interest the interest is added to the balance, and from then on it earns interest too. The longer the money stays, the faster it grows: in the chart above the orange "interest" layer starts thin and ends up bigger than everything you deposited.

Worked example: $10,000 at 5% a year, compounded monthly, for 10 years. Each month the balance grows by 5% ÷ 12 = 0.4167%, 120 times: 10,000 × (1 + 0.05/12)¹²⁰ = $16,470.09. With yearly compounding it would be $16,288.95, with daily compounding $16,486.65: more frequent compounding helps, but much less than a higher rate or more time.

Regular deposits

Most people save a bit every month. Each deposit then grows for a shorter time than the one before it. Adding them all up gives the annuity formula shown above. Example: start with $1,000 and add $100 at the end of every month at 7% (monthly) for 30 years: you put in $37,000 and end with about $130,113.59, so more than $93,000 is interest. Depositing at the start of each month instead earns one more month of interest on every deposit.

APR vs APY (effective annual rate)

The rate a bank quotes (the nominal rate or APR) does not include compounding. The APY (annual percentage yield, also called the effective annual rate, EAR or AER) does: it is how much the balance really grows in one year. 5% compounded monthly is an APY of 5.116%; compounded daily 5.127%. When you compare savings accounts, compare the APY.

Inflation and tax

Inflation makes money buy less over time. If you type an inflation rate, the calculator also shows the final balance in today's money: the balance divided by (1 + inflation)^years. A 5% return with 3% inflation is a real return of only about 2% a year. Tax on interest (outside tax-free accounts such as a TFSA, ISA or Roth IRA) is taken out of the interest each period here, which slows the compounding.

The rule of 72

To estimate how long money takes to double, divide 72 by the yearly rate in percent: at 8% it takes about 72 ÷ 8 = 9 years (exactly 9.01 years with yearly compounding). The rule also works backwards: to double in 6 years you need about 12%. It is most accurate around 6–10%; for continuous compounding 69.3 is the exact number, which is why some people use the "rule of 69" or "rule of 70".

Frequently asked questions

How often is interest compounded in a savings account?: Most banks calculate interest daily and pay it monthly. Choosing "daily" or "monthly" here gives almost the same answer. Bonds and some GICs / CDs compound semi-annually or yearly.
What if my deposit frequency and compounding are different?: The calculator converts the rate to its true yearly growth (the APY) and then to the growth for each deposit period, so weekly deposits with monthly compounding (or any other mix) are handled consistently.
Can I use this for stocks or index funds?: Yes, as a rough plan: type an average yearly return and choose yearly compounding. Real investments go up and down, so the actual result can be much higher or lower; the long-run average of a broad stock index has been around 7% a year after inflation, but nobody can promise future returns.
How do I find how much to save each month?: Open the Goal tab, type the amount you want and choose "How much to deposit". It also tells you how long a plan takes, or what rate you would need.
Why might my bank show a few cents more or less?: Banks round interest to the cent each time they pay it and may count days exactly. This calculator rounds only the amounts it shows, like the textbook formula.
Do you store what I type?: No. Everything is calculated in your browser. Your last numbers are kept only in your own browser, and a shared link simply carries the numbers in its address.

Disclaimer: estimates for information and planning only, not financial or tax advice.

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