How Does Compound Interest Work?

Compound interest is interest that earns interest. Your money grows, and then the growth grows too. Over a few years that loop turns a small gap into a large one. Here is how it works, with a formula and a worked example you can repeat.

The short version: each period your balance earns interest, and that interest joins the balance. Next period the larger balance earns more. Simple interest pays only on your original amount, so it falls behind.

The compound interest formula

One formula gives the future balance. It takes your starting amount, the rate, how often interest is added, and the time.

A = P × (1 + r / n)^{n × t}

Each letter stands for one input:

• A is the final balance you want to find.
• P is the principal, the amount you start with.
• r is the annual rate as a decimal, so 6% is 0.06.
• n is how many times a year interest is added.
• t is the number of years.

A worked example, step by step

Say you put $3,000 in an account that pays 6% a year, added monthly, and leave it for 5 years. Work the formula in order.

1. Write the rate as a decimal: 6% is 0.06.
2. Divide by the periods: 0.06 / 12 = 0.005 per month.
3. Count the periods: 12 months times 5 years is 60.
4. Add one and raise it: 1.005 to the power of 60 is about 1.34885.
5. Multiply by the principal: 3,000 × 1.34885 = 4,046.55.

After 5 years the balance is about $4,046.55. You earned $1,046.55 in interest on your $3,000. With simple interest at the same rate you would earn 3,000 × 0.06 × 5 = $900. Compounding added about $147 more, just from interest earning interest.

Why frequency matters

The same rate compounds harder when it is added more often. Take the same $3,000 at 6% for 5 years, but added once a year instead of monthly. That is 3,000 × 1.06 to the power of 5, which is about $4,014.68.

Monthly compounding reached $4,046.55, so it beat yearly by about $32. The gap is small here, but it widens with bigger balances, higher rates, and longer spans. When you compare two accounts, check how often each one compounds, not just the headline rate.

Time is the strongest lever

Of the four inputs, time does the most work. Early growth becomes the base for later growth, so the curve steepens the longer you wait. A quick way to feel this is the rule of 72. Divide 72 by the rate to estimate the years it takes money to double.

At 6%, that is 72 / 6 = 12 years to double. Wait 24 years and it doubles twice, turning $3,000 into roughly $12,000 before you add a cent. That is why starting early often beats saving more later.

Adding money along the way

The basic formula assumes one deposit that you leave alone. Real savers usually add money over time, and each new deposit starts compounding from the day it lands. So a monthly habit builds two kinds of growth: the new cash you put in, and the interest the whole balance keeps earning.

The order matters less than the consistency. A small amount added every month for years often ends up larger than a bigger sum added late, because the early deposits compound for longer. A calculator handles the running total for you, but the idea is simple: keep feeding the balance and let time do the rest.

Common mistakes to avoid

• Leaving the rate as a percent. Convert 6% to 0.06 before you divide.
• Forgetting to divide by the periods. The exponent and the rate must use the same frequency.
• Setting the exponent to the years. It is periods per year times years, so monthly over 5 years is 60, not 5.
• Mixing up compound and simple interest. Simple pays only on the principal and grows in a straight line.

Frequently asked questions

What is the difference from simple interest? Simple interest pays only on your original amount each period. Compound interest pays on the original plus the interest already added, so it grows faster.

Does compounding work against me on debt? Yes. A credit card balance compounds the same way, so unpaid interest joins the balance and grows. The math that helps a saver can hurt a borrower.

What does APY mean? Annual percentage yield folds the compounding into one yearly figure. It lets you compare accounts on the same basis, whatever their compounding schedule.

Is more frequent compounding always better? For a saver, more often is slightly better at the same rate. The effect shrinks past monthly, so daily and monthly land very close.

Do I have to do this by hand? No. The formula is worth knowing, but a calculator is faster and avoids rounding slips. Use the one below to model any amount, rate, and time in a second.