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.
How to calculate it, step by step
Take 1,000 at 5% a year, compounded monthly, for 10 years, and run the formula. First, the rate per period is r/n = 0.05 / 12 = 0.004167. Second, the number of periods is n x t = 12 x 10 = 120. Third, raise (1 + 0.004167) to the power of 120, which is about 1.647. Finally, multiply by the 1,000 principal to get 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. The US Securities and Exchange Commission offers a free tool that uses this exact formula at Investor.gov.
Does compounding frequency matter?
Yes, but less than people think. At the same annual rate, interest added more often earns slightly more, because each addition starts earning sooner. On 1,000 at 5% for a year, annual compounding gives 50, monthly gives about 51.16, and daily about 51.27. The jump from yearly to monthly is real but small, and from monthly to daily it is tiny. Time and the rate move your balance far more than the frequency does.
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.
The Rule of 72: a quick shortcut
To estimate how long money takes to double without any formula, divide 72 by the annual rate. At 6% money doubles in about 12 years, at 8% in about 9, and at 5% in about 14. It is an approximation, most accurate between roughly 6% and 10%, but it is close enough to do in your head and it makes the effect of a higher rate obvious.
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 do you calculate compound interest?
Use A = P(1 + r/n) to the power of nt. For 1,000 at 5% compounded monthly for 10 years: rate per period 0.05/12, over 120 periods, gives about 1,647. Multiply the principal by (1 + r/n) raised to nt.
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: 1,000 at 5% for a year gives 50 yearly, about 51.16 monthly, and about 51.27 daily.
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.