Compound Interest Calculator

How to use the calculator

1. Initial deposit: the amount you invest today. It can be $0 if you only contribute monthly.
2. Monthly contribution: what you add every month, such as an automatic transfer.
3. Annual interest rate: the nominal yearly rate on a savings account or CD, or the average return you expect.
4. Years: how long the money stays invested.
5. Compounding: how often interest is added: annually, semiannually, quarterly, monthly or daily.
6. Advanced options: deposits at the start or end of each month, and an expected inflation rate to see the result in today's money.

The table and chart show, year by year, how much you contributed and how much came from interest.

How compound interest is calculated

For a single deposit, the classic formula is:

A = P × (1 + r/n)^(n × t)

where P is the principal, r the nominal annual rate as a decimal, n the number of compounding periods per year (1, 2, 4, 12 or 365) and t the number of years.

The calculator simulates month by month. It converts the annual rate into an equivalent monthly growth factor f = (1 + r/n)^(n/12), so the balance grows exactly as under the compounding you selected. Each month the balance is multiplied by f, and the contribution is added at the end of the month (default) or at the start, before growth. For end-of-month deposits this equals the future value of a series of payments:

FV = C × (f^(12t) − 1) / (f − 1)

Here C is the monthly contribution. With monthly compounding f = 1 + r/12, which gives the familiar textbook version. Start-of-month deposits multiply the result by f.

• Effective annual rate = f^12 − 1 = (1 + r/n)^n − 1, the same idea as APY.
• Balance in today's dollars = final balance ÷ (1 + inflation)^t.
• Total contributed includes the initial deposit.

Assumptions: the rate stays constant, nothing is withdrawn, and taxes, account fees and fund expense ratios are not included.

Worked examples

1. Investing $500 a month for 15 years

You start with $10,000, add $500 at the end of every month and earn 8% a year compounded monthly. After 15 years the balance is $206,088.33. You put in $100,000; the other $106,088.33 is interest, and the effective annual rate is 8.30%. Growth speeds up: the balance is $51,636.89 after 5 years and $113,669.42 after 10. With 3% annual inflation, the final amount is worth about $132,280.25 in today's dollars. Making each deposit at the start of the month instead raises the result to $207,241.79.

2. How much does compounding frequency matter?

$1,000 at 5% for 10 years, with no further deposits:

Frequency helps, but far less than a higher rate or more years.

3. The Rule of 72

Dividing 72 by the annual rate gives a rough doubling time. At 8%, 72 ÷ 8 = 9 years, and the calculator confirms that $1,000 compounded annually at 8% reaches $1,999.00 after 9 years. It is only a rule of thumb: it is most accurate for rates of roughly 6% to 10% and drifts further off at very low or very high rates.

How to read your results

Compare total interest with total contributed. Once interest overtakes your deposits, compounding is doing most of the work. That point comes sooner with a higher rate, which is why starting early usually matters more than small differences in the rate.

Treat the result as an estimate. Savings and CD rates change, and investment returns vary and can be negative. Taxes and fees reduce real-world results, and accounts such as 401(k)s and IRAs follow their own tax rules.