Compound interest is the reason small, regular savings can grow into large sums, and the reason credit card debt can spiral. Once you understand how it works, a lot of financial advice suddenly makes sense.
Simple interest vs. compound interest
With simple interest, you earn interest only on the money you put in. $1,000 at 5% earns $50 every year, so after 10 years you have $1,500.
With compound interest, each year's interest is added to your balance and starts earning interest too. In year one you earn $50. In year two you earn 5% of $1,050, which is $52.50. After 10 years you have about $1,629, and the gap keeps widening every year.
The formula
A = P × (1 + r ÷ n)n × t
- A: the amount you end up with
- P: the starting amount
- r: the yearly interest rate as a decimal (5% = 0.05)
- n: how many times a year interest is added (12 for monthly)
- t: the number of years
You don't need to do this by hand. The compound interest calculator does it, including regular monthly contributions, and shows the growth year by year.
Why starting early beats investing more
Compare two savers who both earn 7% a year, compounded monthly:
- Alex invests $200 a month from age 25 to 35, then stops. Total put in: $24,000.
- Sam invests $200 a month from age 35 to 65, thirty years. Total put in: $72,000.
At 65, Alex has about $281,000 and Sam has about $244,000. Alex put in a third as much money and still ends up with more, because Alex's money had an extra ten years to compound.
The rule of 72
To estimate how long it takes money to double, divide 72 by the yearly interest rate:
- At 6%, money doubles in about 72 ÷ 6 = 12 years.
- At 9%, it doubles in about 8 years.
- At 3%, it takes about 24 years.
The same rule works in reverse for inflation: at 3% inflation, prices double in roughly 24 years, so the same money buys half as much.
Compounding works against you on debt
Credit cards often charge 20–30% a year, compounded. By the rule of 72, an unpaid balance at 24% doubles in about three years. That's why paying off high-interest debt is usually the best “investment” available: it's a guaranteed return equal to the interest rate.
How to make compounding work for you
- Start as early as you can, even with small amounts.
- Automate a monthly contribution so it happens without thinking.
- Reinvest dividends and interest instead of withdrawing them.
- Keep fees low: a 1% yearly fee compounds against you just like returns compound for you.
- Pay off high-interest debt before investing.