Simple interest
With simple interest, you earn or pay interest only on the original amount, called the principal. The interest each year is the same, so the balance grows in a straight line.
Here P is the principal, r is the yearly rate as a decimal, and t is the time in years.
Simple interest example
Put $10,000 at 5% simple interest for 10 years. Each year earns $10,000 × 0.05 = $500. After 10 years you have earned $5,000 in interest, for a total of $15,000.
Compound interest
With compound interest, the interest you earn is added to the balance, and the next round of interest is figured on that larger balance. You earn interest on your interest, so growth speeds up over time.
The new letter, n, is how many times per year interest compounds: 1 for yearly, 12 for monthly, 365 for daily.
Compound interest example
Put the same $10,000 at 5% compounded yearly for 10 years: $10,000 × 1.0510 = $16,288.95. That is $1,288.95 more than simple interest, with the same rate and the same money.
Side by side: $10,000 at 5%
The gap is small at first and then widens sharply, because each year's interest is earning interest of its own.
| Method | After 10 years | After 30 years |
|---|---|---|
| Simple interest | $15,000.00 | $25,000.00 |
| Compounded yearly | $16,288.95 | $43,219.42 |
| Compounded monthly | $16,470.09 | $44,677.44 |
| Compounded daily | $16,486.65 | $44,812.29 |
Two lessons stand out. Time matters most: over 30 years, yearly compounding produces more than 70% more than simple interest. How often interest compounds matters much less: going from yearly to daily adds only about $1,600 over 30 years. That is why savings accounts quote an APY, which already folds compounding into one comparable number.
Where you meet each one
Simple interest is common on loans you pay down every month. Most auto loans, for example, are simple interest loans: the CFPB explains that interest is figured on the balance you owe when each payment is due, so paying extra lowers the principal and the interest that follows. Mortgages work similarly, with interest charged each month on the remaining balance.
Compound interest shows up in savings accounts, certificates of deposit, and long-term investments where earnings are reinvested. It also works against you on credit cards, where unpaid interest is added to the balance and then charged interest itself.
- When you save, compounding is your friend. Start early and leave earnings in the account.
- When you borrow, compounding is the lender's friend. Pay credit card balances in full when you can.
- When a loan is simple interest, extra payments toward principal cut the total interest you pay.
A quick way to estimate compound growth
To see roughly how long compounding takes to double your money, divide 72 by the yearly rate. At 5%, that is about 14.4 years. The exact figure is 14.2 years, so the shortcut is close. Our guide to the Rule of 72 explains when it works best.