# Free online compound interest calculator

> Compound interest is interest that earns interest over time. This calculator shows how much a starting deposit plus regular contributions will grow into, year by year.

See how interest compounds on a lump sum or regular contributions over time, with a year-by-year breakdown and support for any compounding frequency.

**Interactive version:** https://onlinecalculator.me/finance/compound-interest/
**Category:** Finance

## How to use

1. Enter your starting balance (can be $0), the annual interest rate, and the time horizon in years.
2. Choose how often interest compounds — monthly is the most common for savings accounts.
3. Add a monthly contribution if you plan to deposit regularly.
4. The calculator shows the final balance, total interest earned, and total amount contributed.
5. Press "Show year-by-year" for a detailed breakdown of growth each year.

## The formula

For a lump sum with no contributions:

```
A = P × (1 + r/n)^(n × t)
```

Where `P` is the starting balance, `r` is the annual rate (as a decimal), `n` is the compounding periods per year, and `t` is the number of years.

When you add monthly contributions, the calculator converts to an **effective monthly rate**:

```
r_monthly = (1 + r/n)^(n/12) − 1
```

Then simulates month-by-month: each month, the balance earns `balance × r_monthly`, then the contribution is added.

## Worked example

Starting with $10,000 at 7% annually, compounded monthly, with $500/month added over 10 years:

- Effective monthly rate: (1 + 0.07/12)^1 − 1 ≈ 0.5833%
- After 10 years (120 months): final balance ≈ **$96,762**
- Total contributions: $10,000 + (120 × $500) = **$70,000**
- Total interest: ≈ **$26,762**

The power of compounding is that more than a quarter of the final balance is pure interest — money that comes from growth, not your deposits.

## Notes

- This calculator uses end-of-period contributions (deposits happen at the end of each month). Some plans use beginning-of-period, which yields slightly more.
- Taxes on interest or dividends reduce real returns. For tax-advantaged accounts (401k, IRA, Roth), the numbers here are more accurate.
- Past stock market returns don't guarantee future results. The 7% figure is often cited as a historical average; actual returns vary year to year.

## Frequently asked questions

### What is the compound interest formula?

The standard formula is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is the compounding periods per year, and t is the time in years. When you add monthly contributions, the calculator simulates month-by-month using an effective monthly rate: (1 + r/n)^(n/12) − 1.

### How does compounding frequency affect growth?

More frequent compounding means interest accrues on interest more often. Daily compounding produces slightly more than monthly, which beats quarterly, which beats annual. The difference is meaningful at high rates or long time horizons — for example, at 7% over 30 years, daily compounding adds about 0.3% to the final balance compared to annual.

### What does "total contributions" include?

It includes the starting principal plus every monthly contribution you make. Total interest is the final balance minus total contributions.

### Can I use this to model a savings account or investment portfolio?

Yes for rough estimates. A savings account typically compounds daily or monthly; index funds compound continuously through reinvested dividends. Use the rate of return you expect and pick the compounding frequency that matches your account.

### How do I share my calculation?

Press "Share with my numbers" — it encodes your inputs in the URL and copies it to your clipboard. Anyone opening the link sees your exact scenario.

## Sources

- [Compound interest](https://en.wikipedia.org/wiki/Compound_interest) — Wikipedia
- [Compound Interest Calculator](https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator) — U.S. Securities and Exchange Commission

## Related calculators

- [Retirement calculator](https://onlinecalculator.me/finance/retirement/) — Uses the same compounding math to project a nest egg with a target retirement age.
- [Loan calculator](https://onlinecalculator.me/finance/loan/) — The flip side of compound interest — how compounding works against you when borrowing.
- [Mortgage calculator](https://onlinecalculator.me/finance/mortgage/) — Fixed-rate mortgage payment and full amortization schedule.
- [Income tax calculator](https://onlinecalculator.me/finance/income-tax/) — US federal income tax with FICA and bracket breakdown for 2024.

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