With simple interest you earn the same amount on your original money every year. With compound interest, each year's gain is added to the balance, so the next year you earn interest on a slightly larger sum. Earning interest on your interest is the whole idea and it's why savings grow faster the longer they're left alone.

CHF 10,000 at 5% per year, nothing added after the first deposit:

The gaps between the bars widen even though the rate never changes. Simple interest would reach just 25,000 over the same 30 years, the extra 18,000 is entirely interest compounding on itself.

1. 1

   Earn interest

   Balance × rate. 10,000 × 5% = 500.

2. 2

   Add it to the balance

   The gain compounds next year, not just the principal. 10,000 + 500 = 10,500.

3. 3

   Repeat on the larger sum

   Each year's interest is a little bigger than the last. 10,500 × 5% = 525.

Three levers, in rough order of how much they matter over a long horizon:

This is why starting early beats waiting for a better return: beginning ten years sooner gives every franc a decade of extra compounding, and that head start is hard to catch by chasing a slightly higher rate later.

Interest can be credited yearly, quarterly, or monthly. Compounding more often means interest starts earning its own interest a little sooner, so the final balance is slightly higher. The effect is real but small, the number of years matters far more than how often interest is added within each year.

The same maths works against you just as reliably:

• —Inflation compounds against your balance. A 5% return with 2% inflation grows real wealth at closer to 3%.
• —Fees compound too, a yearly percentage quietly shrinks the balance every single year.
• —Debt runs the same curve in reverse. A credit-card balance compounds against you at rates far above any investment.