How compound interest works, explained with a whiteboard video

Compound interest is interest that earns interest. Each time the bank adds interest to your balance, the next round is worked out on the bigger number. So the growth speeds up the longer you leave the money alone.

Here's the 90-second version, then the same idea worked through with real numbers.

Simple interest vs compound interest

Put $1,000 in two jars, each earning 5% a year.

Simple interest pays 5% of the original $1,000 every year: $50, then another $50. After two years the jar holds $1,100.

Compound interest pays 5% of whatever is in the jar. Year one adds $50, the same as before. Year two adds 5% of $1,050, which is $52.50. After two years the jar holds $1,102.50.

Two and a half dollars is easy to shrug off. Here's the same gap at 7% over longer stretches:

Years at 7%	Simple interest	Compound interest
10	$1,700	$1,967
20	$2,400	$3,870
30	$3,100	$7,612

Simple interest grows in a straight line. Compound interest curves upward, and after 30 years it's more than double.

The compound interest formula

A = P(1 + r/n)^(nt)

A is the amount you end up with
P is the principal, the money you start with
r is the yearly interest rate as a decimal (5% is 0.05)
n is how many times a year interest is added
t is the number of years

Check it with the jars. $1,000 at 5%, added once a year, for two years:

A = 1000 × (1 + 0.05/1)^(1 × 2) = 1000 × 1.1025 = 1102.50

Same $1,102.50 as before. The formula just does the year-by-year adding in one step.

If you only want the interest earned, subtract the starting money: A − P, which here is $102.50.

How often it compounds matters

The n in the formula is the compounding frequency. More often means interest starts earning interest sooner. Here's $1,000 at 5% for 10 years:

Compounded	Balance after 10 years
Yearly	$1,628.89
Quarterly	$1,643.62
Monthly	$1,647.01
Daily	$1,648.66

Going from yearly to monthly adds about $18. Going from monthly to daily adds less than $2. So when you compare savings accounts, the rate matters far more than the schedule, which is why banks quote the APY (annual percentage yield): it already includes the compounding.

Compound interest works against you on debt

The same maths runs on what you owe. A $2,000 credit card balance at 20% a year, compounded monthly, grows to about $2,438.78 after one year if you pay nothing. That's $438.78 of interest, more than the $400 simple interest would charge, because each month's interest gets charged interest too.

So pay down expensive debt first: every month you wait, the balance you're paying interest on gets bigger.

The Rule of 72

To guess how long money takes to double, divide 72 by the yearly interest rate.

Rate	Rule of 72	Exact
6%	12 years	11.9 years
8%	9 years	9.0 years
10%	7.2 years	7.3 years

It's a mental shortcut, not the formula, but between about 6% and 10% it lands within a few months. It works for debt too: at 24%, a balance you ignore doubles in about three years.

Common mistakes

Typing the rate as a whole number. 5% goes into the formula as 0.05, not 5.
Forgetting the exponent is n × t. Monthly for 10 years is 120 compounding periods, not 10.
Comparing a rate with an APY. A 4.9% rate compounded daily and a 5% APY are close to the same deal. Compare APY with APY.
Starting late. Most of the growth comes in the later years. In the 30-year row of the first table, more than half the balance is interest earned on earlier interest.

How this video was made

The video at the top was made with Rekka from the topic "How compound interest works". Rekka researched the topic and wrote the script. It drew the jars and the money tree in the order the narrator names them, and lettered the formula line by line as it's spoken. You can make one for your own topic the same way.