📈 Compound Interest Calculator
Project how a lump sum plus regular monthly contributions grows over time at a fixed annual rate. Useful for savings accounts, CDs and simple investment projections.
How the projection is built
For a lump sum on its own, compound growth is a single expression, where
r is the annual rate as a decimal, n the number of
compounding periods per year and t the years:
A = P x (1 + r/n)^(n x t)Adding a monthly contribution breaks that neat form, because each deposit compounds for a different length of time. So this calculator steps through the period month by month instead: your contribution goes in at the start of the month, and interest is applied whenever a compounding period closes. That handles every frequency correctly, including the awkward case where quarterly or annual compounding does not line up with monthly deposits.
Compounding frequency matters less than people expect
$10,000 left alone for 20 years at 7%, by frequency:
| Compounding | Final balance |
|---|---|
| Annually | $38,697 |
| Quarterly | $40,064 |
| Monthly | $40,387 |
| Daily | $40,547 |
The whole span from annual to daily is about $1,850 over twenty years, and the gap between monthly and daily is $160. Chasing a daily-compounding account is rarely worth it. The rate, the amount you add each month, and the number of years are the levers that actually move the result.
Where the money comes from
Run the defaults — $10,000 to start, $200 a month, 7%, 20 years — and you finish near $145,000 having paid in $58,000. Interest is roughly 60% of the final balance. That share is almost entirely a function of time: the same contributions over ten years instead of twenty leave interest at under a third of the total, because the early deposits have not had long enough to compound.
What the projection leaves out
- Tax. Interest in a taxable account is usually taxed as it is earned, which quietly lowers the effective rate.
- Inflation. The result is in future dollars, not today's.
- Fees. A 0.5% expense ratio comes straight off the rate.
- Variable returns. Real markets do not deliver 7% every year, and the order of good and bad years matters once you start withdrawing.
Frequently asked questions
What is the compound interest formula?
A = P x (1 + r/n)^(n x t), where P is the starting amount, r the annual rate as a decimal, n the compounding periods per year and t the years. Once you add regular contributions there is no equally tidy closed form, which is why this tool simulates month by month.
Does daily compounding beat monthly by much?
Almost never. $10,000 at 7% for 20 years grows to $40,547 compounded daily against $40,387 compounded monthly — about $160 across two decades. A rate that is a tenth of a percent higher is worth more than the frequency.
Are contributions added before or after interest?
Before. Each monthly contribution is deposited at the start of the month, so it earns that period's interest. Accounts that credit deposits at the end of the month will run very slightly behind this projection.
Is a 7% return realistic?
As a long-run nominal average for a diversified stock portfolio, yes; for a savings account or CD it is not. Use the rate that matches the product you are actually modelling — a high-yield savings account is closer to 4%, and a bond fund somewhere between.
Does this account for tax or inflation?
Neither. The figure is pre-tax and in future dollars. For a rough inflation-adjusted view, subtract your expected inflation rate from the return before entering it, which gives an answer in today's purchasing power.