Simple interest is computed on the original amount only. The formula is I = Prt, with r a decimal and t in years.
Step 1: Let's Learn
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Compound interest
Compound interest is computed on the balance, which includes interest already earned. Interest starts earning interest.
The formula
A = P(1 + r/n)^(nt), where n is the number of compoundings per year.
The gap grows
Over one year the two barely differ. Over thirty years compound interest leaves simple interest far behind.
Time matters most
Because the exponent is time, starting early beats saving more later. Ten years of head start is difficult to catch.
It works against you too
Credit card debt compounds exactly the same way. The mathematics does not care which side you are on.
Simple interest
I = Prt: principal times rate times time. Interest is computed on the original amount only, so it grows linearly. Some short-term loans work this way, and it is the easier case to compute.
Compound interest earns on interest
Interest is added to the balance and then itself earns interest. Growth is exponential rather than linear, and over long periods the difference between the two is enormous rather than marginal.
Compounding frequency matters
The same annual rate compounded monthly yields more than compounded yearly, because interest starts earning sooner. That is why the stated rate and the effective annual rate are different numbers.
It works against you too
Compound interest builds savings and also builds debt. On a credit card balance, the same mechanism that makes long-term saving powerful makes carried debt expensive. The arithmetic does not care which side you are on.
Step 2: Try It Yourself
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Step 3: Watch an Example
One step at a time.
Watch Ines Compare Both Kinds
$1000 at 10% a year for 3 years, simple against compound.
- Step 1
Simple interest gives 1000 × 0.10 × 3 = $300, so the total is $1300.
Step 4: Your Turn
Practice makes it stick.
The Simple Case
Problem 1 of 2
$2000 at 5% simple interest for 3 years. Interest earned, in dollars?
dollars
The Compound Case
Problem 2 of 2
$1000 at 10% compounded annually for 2 years. Final balance in dollars?
dollars
Grow the Money
1 of 8
$1000 at 6% simple for 2 years. Interest in dollars?
2 of 8
$5000 at 4% simple for 3 years. Interest in dollars?
3 of 8
$1000 at 10% compounded annually for 3 years. Balance in dollars?
4 of 8
$2000 at 50% compounded annually for 2 years. Balance in dollars?
5 of 8
$1000 at 10% simple for 3 years. Balance in dollars?
6 of 8
Which grows faster over 30 years? 1 simple, 2 compound.
7 of 8
Sort each statement by which kind of interest it describes.
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- Empty
- Empty
8 of 8
$4000 at 5% simple for 4 years. Interest in dollars?
Step 5: Quick Check
Show what you know.
Question 1 of 2
$3000 at 5% simple for 2 years. Interest in dollars?
Question 2 of 2
What makes compound interest different?
What You Learned
- Simple interest is I = Prt, computed on the original amount.
- Compound interest is computed on the balance, so interest earns interest.
- Time is the most powerful factor, because it sits in the exponent.