# What will compound interest earn?

Computes the balance of savings that earn compound interest, with optional monthly top-ups, and how much of it is interest.

- Page: https://www.acalculator.org/finance/compound-interest-calculator
- JSON spec: https://www.acalculator.org/finance/compound-interest-calculator.json
- Version: 31dd1260cad8

## Default answer

Example with the default inputs (Starting amount $10,000.00, Regular top-up $0.00, Interest rate 5%, For how long? (years) 10, How often is interest added? Monthly, Start date October 5, 2026, Prices rise each year by 3%) on the example date Monday, October 5, 2026: $10,000.00 now for 10 years at 5% a year grows to $16,470.09, of which $6,470.09 is interest.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| principal | Starting amount | The amount saved today, at the start. |
| add | Regular top-up | A top-up added at the end of every month. A yearly amount is split into 12 equal monthly top-ups. |
| rate | Interest rate | The nominal yearly interest rate. |
| years | For how long? (years) | How many years the money grows. |
| comp | How often is interest added? | How many times a year interest is added to the balance: monthly (12), quarterly (4), or yearly (1). |
| start | Start date | The day the savings start. It labels the months and gives the end date. |
| inflation | Prices rise each year by | The yearly inflation rate used to show the balance in today’s money. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| fv | You’ll have | The balance at the end of the last month. |
| plan | Your savings plan | The starting amount, the monthly top-up, and the number of years, in words. |
| paidIn | Your money | The starting amount plus every top-up. |
| interest | Interest | All the interest earned: the final balance minus your money. |
| lastYear | Interest in the last year | The interest earned in the final 12 months. |
| doubling | Years to double your money | How many years a balance takes to double at this rate with no top-ups: ln 2 ÷ ln(1 + yearly effective rate). |
| real | In today’s money | The final balance divided by (1 + inflation) to the power of the years. |
| end | Ends in | The month of the final balance, when a start date is given. |

## Method

Each month, add interest at the monthly rate (1 + r/m)^(m/12) − 1, where r is the yearly rate and m the compounding times a year, then add the top-up.

## Assumptions

- The rate does not change.
- Top-ups are added at the end of each month; a yearly top-up is split into 12 equal monthly ones.
- With quarterly or yearly compounding, interest builds at the equivalent monthly rate, so the balance matches A = P(1 + r/m)^(mt) at every compounding date.
- Tax and fees are not included.
- “In today’s money” divides the final balance by (1 + inflation)^years.

## Worked examples

1. principal = $10,000.00, rate = 5%, years = 10, comp = 12 gives fv = $16,470.09, interest = $6,470.09. Source: SEC Investor.gov formula A = P(1 + r/n)^(nt).
2. principal = $1,000.00, rate = 5%, years = 10, comp = 1 gives fv = $1,628.89.
3. principal = $0.00, add = $100.00, rate = 6%, years = 10, comp = 12 gives fv = $16,387.93, paidIn = $12,000.00.
4. principal = $10,000.00, rate = 6%, years = 5, comp = 1, start = 2026-10-01 gives fv = $13,382.26, doubling = 11.895661, end = 2031-10-01.

## FAQ

### What is compound interest?

Compound interest is interest earned on both the principal amount and any previously earned interest. Unlike simple interest, compound interest grows exponentially over time, making it a powerful tool for long-term investments and savings. The interest you earn each period is added to your principal, so you earn interest on your interest.

### How do I calculate compound interest?

The compound interest formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time in years. For example, $1,000 at 5% compounded annually for 10 years becomes $1,000(1 + 0.05/1)^(1×10) = $1,628.89.

### What's the difference between simple and compound interest?

Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal and any previously earned interest. Simple interest grows linearly, while compound interest grows exponentially. For example, $1,000 at 5% simple interest for 10 years earns $500 total, while compound interest earns $628.89.

### How often should interest be compounded?

The more frequently interest is compounded, the more you'll earn. Daily compounding provides the highest returns, followed by monthly, quarterly, and annually. For example, $1,000 at 5% for 10 years: annually = $1,628.89, monthly = $1,647.01, daily = $1,648.66.

### What is the Rule of 72?

The Rule of 72 is a quick way to estimate how long it takes for an investment to double. Divide 72 by the annual interest rate to get the approximate number of years. For example, at 6% interest, it takes about 12 years to double your money (72 ÷ 6 = 12). At 8%, it takes about 9 years (72 ÷ 8 = 9). The calculator above gives the exact figure: ln 2 ÷ ln(1 + rate).

### How does compound interest affect debt?

Compound interest works against you with debt. Credit cards and loans use compound interest, meaning you pay interest on both the principal and accumulated interest. This is why it's important to pay off high-interest debt quickly. For example, a $1,000 credit card balance at 18% APR, compounded monthly, grows to over $2,000 in 4 years if no payments are made.

### What is continuous compounding?

Continuous compounding is when interest is calculated and added to the principal an infinite number of times per year. The formula is A = Pe^(rt), where e is Euler's number (approximately 2.718). While theoretical, it's used in some financial models and provides the maximum possible compound growth.

### How do I calculate compound interest with regular contributions?

For regular contributions, use the future value of an annuity formula: FV = PMT × [(1 + r)^n - 1] / r, where PMT is the regular payment, r is the interest rate per period, and n is the number of periods. Add this to the compound interest on your initial principal for the total future value.

### What is the effective annual rate (EAR)?

The effective annual rate is the actual interest rate earned when compounding is considered. EAR = (1 + r/n)^n - 1, where r is the nominal rate and n is compounding frequency. For example, 5% compounded monthly has an EAR of (1 + 0.05/12)^12 - 1 = 5.12%.

### How does inflation affect compound interest?

Inflation reduces the real value of compound interest returns. To estimate real returns, subtract the inflation rate from the nominal interest rate. For example, if you earn 6% interest but inflation is 2%, your real return is roughly 4% (exactly 1.06 ÷ 1.02 − 1 = 3.92%). This is why it's important to consider inflation when planning long-term investments.

## Sources

- U.S. Securities and Exchange Commission, Investor.gov compound interest calculator and formula. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
- Future value of an annuity and effective annual rate: S. A. Broverman, Mathematics of Investment and Credit, chapters 1 and 2.