With simple interest you earn (or owe) interest only on the original amount, so the balance grows by the same sum every year: a straight line. With compound interest each period's interest is added to the balance and earns interest itself, so growth accelerates: a curve. Over a year or two the difference is small; over decades it is enormous. Compounding is what you want on savings and investments and what you must watch out for on debt.
At a glance
| Property | Simple interest | Compound interest |
|---|---|---|
| Interest is charged on | The original principal only | Principal plus all interest already added |
| Formula | A = P × (1 + r × t) |
A = P × (1 + r/n)^(n × t) |
| Growth pattern | Linear: the same amount each year | Exponential: a bigger amount each year |
| Effect of compounding frequency | None | More frequent compounding pays a little more |
| Time to double at 5% a year | 20 years | About 14.2 years (annual compounding) |
| Common uses | Short-term loans, some auto and personal loans, bond coupon payments | Savings accounts, CDs, investments, credit card balances, reinvested dividends |
In the formulas A is the final amount, P the principal, r the annual rate as a decimal, t the number of years and n the number of compounding periods per year.
Worked example: $10,000 at 5%
| Years | Simple interest | Compound, annually | Compound, monthly | Compound advantage (annual) |
|---|---|---|---|---|
| 1 | $10,500.00 | $10,500.00 | $10,511.62 | $0.00 |
| 2 | $11,000.00 | $11,025.00 | $11,049.41 | $25.00 |
| 5 | $12,500.00 | $12,762.82 | $12,833.59 | $262.82 |
| 10 | $15,000.00 | $16,288.95 | $16,470.09 | $1,288.95 |
| 20 | $20,000.00 | $26,532.98 | $27,126.40 | $6,532.98 |
| 30 | $25,000.00 | $43,219.42 | $44,677.44 | $18,219.42 |
After one year with annual compounding the two are identical, because no interest has been added yet. After 30 years, compounding has turned $15,000 of simple interest into $33,219.42, more than twice as much. Monthly compounding adds a little more on top; that difference is what APY captures (5% compounded monthly is an APY of about 5.12%).
Check these figures or try your own with the Simple Interest Calculator and the Compound Interest Calculator.
Simple interest
Simple interest is easy to calculate and to predict: interest = principal × rate × time. It is common where the term is short or the interest is paid out rather than reinvested: bond coupons, some short-term business and personal loans, and payday-style or "add-on" loan quotes. Many amortizing loans also behave this way, because each month's interest is charged on the balance still owed and paid off immediately.
Simple interest is better for you when you are the borrower: on a debt where unpaid interest is never added to the balance, you pay less than under compounding.
Compound interest
Compound interest rewards time. The longer money stays invested and the more often interest is added, the faster it grows; the Rule of 72 Calculator estimates doubling time as 72 divided by the rate (72 ÷ 5 = 14.4 years, close to the exact 14.2). It works against you on revolving debt: $5,000 on a card at 20% a year compounded monthly, with nothing paid, grows to about $9,065.65 in three years, against $8,000.00 with simple interest.
Compound interest is better for you when you are the saver or investor: pick accounts that compound often, compare them by APY with the APY Calculator, and reinvest returns rather than withdrawing them.
Which should you choose?
You rarely get to choose the method, but you can choose products and habits:
- Saving or investing: look for compounding (and compare APY, not the nominal rate); start early and leave returns invested.
- Borrowing: prefer loans where interest is not capitalised, and pay at least the interest due so it never compounds.
- Comparing two offers: convert both to an effective annual rate before deciding.
- Quick estimates: simple interest for short periods, the rule of 72 for long ones.
For the compounding formula in depth, continuous compounding and regular deposits, see How Compound Interest Works.