# Compound Interest Calculator

> Compound interest is interest earned on both your deposits and the interest already added to them. $10,000 at 5% compounded monthly grows to $16,470.09 in 10 years, and adding $100 a month lifts the total to $31,998.32. Enter your own numbers to see the balance, APY and formula.

- Interactive calculator: https://calculatorswithsteps.com/compound-interest-calculator
- Category: Financial Calculators
- Last updated: 2026-11-10
- Publisher: Calculators With Steps (calculatorswithsteps.com)

## How to use the compound interest calculator

1. **Initial deposit** – the amount you start with.
2. **Regular contribution** – how much you add each month or each year. Leave it at 0 for a single lump sum.
3. **Annual interest rate** – the nominal yearly rate (APR) on the account or your expected return.
4. **Time period** – how many years the money stays invested.
5. **Compounding frequency** – daily (365), monthly, quarterly, semiannually or annually. Bank accounts often compound daily or monthly; many bonds and CDs compound semiannually or annually.
6. **Contribution timing** – deposits at the end of each period (the usual assumption) or at the start.

The result shows the final balance, the split between your deposits and interest, the effective annual yield and a year-by-year table. The step-by-step working shows every number in the formula.

## The compound interest formula

For a single deposit:

**A = P(1 + r/n)^nt**

- **A** = final amount
- **P** = principal (initial deposit)
- **r** = annual interest rate as a decimal (5% = 0.05)
- **n** = compounding periods per year
- **t** = number of years

Regular contributions are added with the future value of a series:

**FV = PMT × [(1 + i)^N − 1] ÷ i**

where i is the rate per contribution period and N is the number of contributions. For deposits at the start of each period, multiply by (1 + i). When contributions and compounding happen at different frequencies (for example monthly deposits with quarterly compounding), the calculator converts the rate to an equivalent rate per contribution period: i = (1 + r/n)^(n/p) − 1, where p is the number of contributions per year.

## Worked example

Start with $10,000, add $100 at the end of every month, earn 5% compounded monthly for 10 years:

| Part | Calculation | Value |
| --- | --- | --- |
| Initial deposit | 10,000 × (1 + 0.05/12)^120 | $16,470.09 |
| Monthly deposits | 100 × [(1.0041667)^120 − 1] ÷ 0.0041667 | $15,528.23 |
| **Final balance** | | **$31,998.32** |
| Total deposited | $10,000 + 120 × $100 | $22,000.00 |
| Interest earned | | $9,998.32 |

Make the same deposits at the start of each month instead and the balance rises to $32,063.02, because each deposit earns one extra month of interest. Leave everything in place for 30 years and the balance reaches about $127,903 on $46,000 of deposits.

## How compounding frequency affects growth

$10,000 at a 5% nominal rate for 10 years, no contributions:

| Compounding | Final balance | APY |
| --- | --- | --- |
| Annually | $16,288.95 | 5.000% |
| Semiannually | $16,386.16 | 5.062% |
| Quarterly | $16,436.19 | 5.095% |
| Monthly | $16,470.09 | 5.116% |
| Daily | $16,486.65 | 5.127% |

More frequent compounding helps, but the gains shrink quickly. Moving from monthly to daily adds less than $17 over ten years. When comparing savings accounts, look at the APY, which already includes compounding. U.S. banks must disclose it under the Truth in Savings rules.

## Common compound interest mistakes

- **Using the annual rate per period.** In the formula, the rate is divided by the number of compounding periods. Plugging 5% into a monthly formula without dividing by 12 gives a wildly wrong answer.
- **Mixing up APR and APY.** If a bank quotes an APY, it already includes compounding. Enter it with annual compounding, or use the [savings calculator](https://calculatorswithsteps.com/savings-calculator), which works from APY directly.
- **Forgetting when deposits happen.** Deposits at the start of each period earn one extra period of interest. Spreadsheet functions like FV assume end-of-period payments unless you set the type argument to 1.
- **Ignoring compounding on debt.** The same math works against you on credit cards and loans, where unpaid interest is added to the balance.

## Getting the most from compound interest

- **Start early.** Time is the exponent in the formula, so extra years matter more than a slightly higher rate.
- **Keep contributing.** In the example, the steady $100 deposits grow to $15,528.23, almost half of the final balance.
- **Watch fees and taxes.** A 1% annual fee reduces the rate in the formula one for one.
- **Use the right tool.** For bank savings quoted as an APY, use the [savings calculator](https://calculatorswithsteps.com/savings-calculator). For stock-market investing with rising contributions and inflation, use the [investment calculator](https://calculatorswithsteps.com/investment-calculator). To see what interest looks like without compounding, try the [simple interest calculator](https://calculatorswithsteps.com/simple-interest-calculator).

## Frequently asked questions

### What is the formula for compound interest?

A = P(1 + r/n)^(nt), where P is the starting amount, r is the annual rate as a decimal, n is the number of compounding periods per year and t is the number of years. Interest earned is A − P.

### How do you calculate compound interest for 3 years?

Apply the formula with t = 3. For $5,000 at 8% compounded annually, A = 5,000 × 1.08^3 = $6,298.56, so the interest is $1,298.56. Compounded half-yearly, it is 5,000 × 1.04^6 = $6,326.60.

### Is daily compounding much better than monthly?

Only slightly. $10,000 at 5% for 10 years grows to $16,470.09 with monthly compounding and $16,486.65 with daily compounding, a difference of $16.56. The rate itself matters far more than the compounding frequency.

### How do I calculate compound interest in Excel with monthly contributions?

Use =FV(rate/12, years*12, -monthly, -initial). For example, =FV(5%/12, 120, -100, -10000) returns 31,998.32, which matches this calculator with monthly compounding and end-of-month deposits.

### What is the difference between APR and APY?

APR is the stated annual rate before compounding. APY is what you actually earn in a year once compounding is included: APY = (1 + r/n)^n − 1. A 5% rate compounded monthly is a 5.116% APY.

### How long does it take money to double with compound interest?

Divide 72 by the annual rate for a quick estimate. At 5%, the rule of 72 gives 14.4 years; the exact answer with annual compounding is 14.2 years, and about 13.9 years with monthly compounding.

### What is the difference between simple and compound interest?

Simple interest is paid only on the original principal, so it grows in a straight line. Compound interest is also paid on past interest. Over 10 years at 5%, $10,000 earns $5,000 of simple interest but $6,288.95 compounded annually.

## Sources

- [Wikipedia – Compound interest](https://en.wikipedia.org/wiki/Compound_interest)
- [CFPB – Regulation DD, Appendix A (annual percentage yield formula)](https://www.consumerfinance.gov/rules-policy/regulations/1030/appendix-A/)

> Disclaimer: results are estimates for information and education, not financial advice. Confirm important decisions with a qualified professional.