How compound interest works

Simple versus compound

Simple interest is calculated on the original amount every period. $1,000 at 5% simple interest earns $50 a year, every year, forever. After 30 years: $2,500.

Compound interest is calculated on the balance, including interest already earned. Year one earns $50. Year two earns 5% of $1,050, which is $52.50. Year three earns 5% of $1,102.50. After 30 years: about $4,322.

Same rate, same starting amount, same period. The $1,822 difference is entirely the compounding.

A = P × (1 + r ÷ n)^(n × t)

Time is the dominant variable

The exponent is where the effect lives, and time sits in the exponent. That makes the relationship between years and outcome distinctly non-linear.

$10,000 at 6%, left alone:

The first decade adds about $7,900. The fourth adds about $45,000. Nothing changed except the size of the base each year's interest is calculated on.

This is the entire argument for starting early, and it is a stronger argument than any about rate selection.

Frequency matters much less than people think

Daily compounding sounds meaningfully better than annual. It is not.

At 5%, compounding annually produces an effective 5.00%. Compounding daily produces 5.13%. That is the whole difference, and there is a hard ceiling: continuous compounding at 5% gives 5.127%, which is the mathematical limit. No frequency can beat it.

So when comparing accounts, compare the APY, which already includes whatever frequency the provider uses. The frequency itself is not a variable worth optimizing.

Contributions usually do more than compounding

Over a working lifetime, compounding dominates. Over five or ten years — the horizon most savings goals actually have — regular deposits do most of the work.

$5,000 at 4.5% over ten years grows to about $7,800. The same $5,000 with $200 a month added grows to about $38,000. Of that $38,000, roughly $29,000 is money you put in.

Both matter. But if you are choosing between finding a slightly better rate and increasing your monthly deposit, the deposit wins on any short or medium horizon. The savings goal calculator will tell you exactly what deposit reaches a specific target by a specific date.

Inflation compounds too

A balance growing at 4% while prices rise at 3% is gaining about 1% a year in purchasing power, not 4%.

Real value = future balance ÷ (1 + inflation)^years

Our compound interest calculator has an inflation field for exactly this reason. Entering a rate shows you the projected balance in today's money alongside the nominal figure. On a thirty-year horizon the two numbers are very far apart, and only one of them tells you what you can buy.

It works against you identically

There is nothing special about savings. The same mechanism runs on debt.

A credit card balance at 22% APR, with interest applied daily and unpaid interest joining the balance, compounds exactly as a savings account does — just in the wrong direction, and usually at four or five times the rate any deposit account pays.

Which is why clearing high-interest debt beats optimizing a savings rate almost every time. A guaranteed 22% return is available to anyone carrying a card balance, and no savings account will match it. See how credit card interest works.