Compound interest explained: how money grows on itself
By Johannes Nieuwboer · 6 min read
Compound interest means you earn interest not only on the money you put in, but also on the interest that money has already earned. Over short periods the difference with simple interest is small; over decades it becomes the single biggest factor in how large savings or debts grow.
Simple vs. compound interest
With simple interest, you earn a fixed percentage of your original deposit every year. Put $1,000 in an account paying 5% simple interest and you earn $50 per year, every year. After 20 years you have $2,000.
With compound interest, each year's interest is added to the balance, and next year's interest is calculated on that larger balance. The same $1,000 at 5% compounded yearly becomes $1,050 after one year, $1,102.50 after two, and about $2,653 after 20 years — roughly $650 more than simple interest, without adding a cent.
The formula
The standard formula is A = P × (1 + r/n)^(n × t). P is the starting amount, r the yearly interest rate as a decimal, n the number of times interest is added per year, and t the number of years. A is the final amount.
Example: $5,000 at 4% compounded monthly for 10 years gives A = 5,000 × (1 + 0.04/12)^(120) ≈ $7,454. Compounded yearly instead, it would be about $7,401. More frequent compounding helps a little; the rate and the time help far more.
The Rule of 72
A quick mental shortcut: divide 72 by the yearly interest rate to estimate how many years it takes for money to double. At 6% that is about 12 years; at 9% about 8 years; at 3% about 24 years.
The rule works in reverse for costs too. If prices rise 4% a year, the value of cash halves in roughly 18 years — which is why inflation matters when you compare returns.
Why time beats amount
Imagine two savers earning 6% a year. Anna saves $200 a month from age 25 to 35 and then stops. Ben saves $200 a month from 35 to 65. Anna paid in $24,000, Ben $72,000 — yet at 65 Anna's balance is comparable to Ben's, because her money had thirty extra years to compound.
The lesson is not that late starters should give up, but that every extra year counts. Regular contributions plus time do most of the work.
Compounding works against you on debt
Credit cards and some loans compound too. An unpaid balance at 20% a year grows by about 22% when compounded monthly. Paying off high-interest debt is effectively a guaranteed return equal to that rate, which is hard to beat with any investment.
Returns on real investments are never guaranteed and vary year to year; calculators use a steady rate to show the principle, not to predict the future.