Compound Interest Explained (With Examples)
Compound interest is often called the most powerful force in personal finance, and for once the hype is fair. It is the reason a modest amount saved young can outgrow a much larger amount saved later. Here is how it actually works.
What compound interest is
Simple interest pays you only on your original deposit. Compound interest pays you on your deposit and on the interest you have already earned. Each period builds on the last, so your balance does not grow in a straight line, it curves upward and gets steeper over time.
The formula
A = P (1 + r/n) raised to the power of n x t, where P is your starting amount, r is the annual rate as a decimal, n is how many times a year interest is added, and t is the number of years.
A worked example
Put 1,000 in an account paying 5% a year, compounded monthly, and leave it for 10 years. It grows to about 1,647, so you earn roughly 647 without adding a single extra cent. Leave that same 1,000 for 30 years and it becomes about 4,468. Tripling the time more than quadrupled the interest, because the later years compound on a much bigger balance.
Simple vs compound
Over one year the two barely differ. Over decades the gap is enormous. That widening gap is the whole point: the longer money compounds, the more of your final balance is growth rather than your own contributions.
Why starting early beats saving more
Because the earliest money compounds the longest, when you start often matters more than how much you save. Someone who saves for ten years and then stops can end up ahead of someone who starts ten years later and saves for far longer. Time is the ingredient you cannot buy back.
Try it with your own numbers
See it for yourself with the Compound Interest Calculator. To add regular monthly contributions, use the Investment Calculator, or work backward from a target with the Savings Goal Calculator.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus interest already earned, so it grows faster over time.
How often should interest compound?
For savings, more often is better. Daily beats monthly beats yearly at the same rate, though the difference is small at modest rates.
Why does starting early matter so much?
The earliest money compounds the longest, so it grows the most. Starting ten years sooner can roughly double the final amount for the same monthly saving.