# Compound interest calculator

> Compound interest adds each period's interest to the balance, so interest starts earning interest. The formula is A = P × (1 + r ÷ n)^(n × t). Starting with $10,000 at 5% a year, compounded monthly for 10 years, the balance reaches $16,470.09, which includes $6,470.09 of interest. Monthly deposits are supported too.

Source: https://www.calterix.com/en-us/calculator/compound-interest/ · Updated 11/06/2026 · en-US

## How compound interest works

Each period, interest is figured on the starting amount plus all the interest earned so far. That "interest on interest" makes the balance grow faster every year.

```
A = P × (1 + r ÷ n)^(n × t)
With monthly deposits: A = P × (1 + i)^m + D × [(1 + i)^m − 1] ÷ i
```
P is the starting amount, r the yearly rate as a decimal (5% = 0.05), n the compounding periods per year, t the years, D the monthly deposit, m the months, and i the monthly rate.

Example: $10,000 at 5% compounded monthly for 10 years. The monthly rate is 0.05 ÷ 12, and 120 months later the balance is 10,000 × (1.004167)^120 = $16,470.09.

With deposits, the calculator converts the rate to an equivalent monthly rate and assumes each deposit lands at the end of the month. For compounding that is not monthly, that keeps the yearly growth the same as the rate you picked.

## Daily, monthly, quarterly, or yearly compounding

The more often interest compounds, the more you earn, though the gain shrinks quickly. Going from yearly to monthly adds a lot more than going from monthly to daily.

| Compounded | Balance after 10 years | Effective yearly rate (APY) |
| --- | --- | --- |
| Yearly | $16,288.95 | 5.00% |
| Quarterly | $16,436.19 | 5.09% |
| Monthly | $16,470.09 | 5.12% |
| Daily | $16,486.65 | 5.13% |

$10,000 at a 5% yearly rate.

APR is the stated yearly rate. APY includes the effect of compounding, so APY is the better number for comparing savings accounts. To compare with interest that never compounds, see the [simple interest calculator](https://www.calterix.com/en-us/calculator/simple-interest/).

## The rule of 72: how long to double your money

Divide 72 by the yearly rate to estimate the years it takes for a balance to double. At 6%, that is about 72 ÷ 6 = 12 years.

| Yearly rate | Rule of 72 | Exact (yearly compounding) |
| --- | --- | --- |
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |

The rule is a shortcut and lands close for rates from about 4% to 12%.

> Rates in the examples are only examples. Real savings and investment returns change, and past returns do not promise future ones. Fees and taxes are not included.

## Frequently asked questions

### What is the compound interest formula?

A = P × (1 + r ÷ n)^(n × t), where P is the starting amount, r the yearly rate as a decimal, n the compounding periods per year, and t the years.

### How do I calculate compound interest with monthly deposits?

Add the future value of the deposits: D × [(1 + i)^m − 1] ÷ i. Use the monthly deposits tab. $500 a month at 6% for 1 year grows to $6,167.78.

### How often does interest compound?

It depends on the account. Savings accounts often compound daily or monthly, and some bonds and CDs compound less often. Check the account terms.

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

APR is the stated yearly rate. APY adds the effect of compounding. A 5% APR compounded monthly has an APY of about 5.12%.

### How do I calculate daily compound interest?

Set compounding to daily. At 5% on $10,000 for 10 years, the balance is $16,486.65. The daily rate is the yearly rate ÷ 365.

### How long does it take to double my money?

Divide 72 by the yearly rate for a quick estimate. At 6%, that is about 12 years. The exact figure is 11.9 years.