Interest Rate vs Compound Interest
Interest Rate and Compound Interest are two Money, Banking & Finance concepts in AP Economics that students often mix up. An interest rate is the cost of borrowing money or the reward for saving it, expressed as a percentage of the principal per year. Compound interest is interest earned on both the original principal and on previously accumulated interest. Here is how they compare side by side.
Interest rates are set in money and loanable-funds markets and steered by the central bank. Lower rates encourage borrowing, investment, and spending; higher rates encourage saving and slow the economy. The real interest rate (nominal minus inflation) reflects the true cost of borrowing.
Because interest is added back to the balance, savings grow faster over time than with simple interest. The longer the time horizon and the higher the rate, the larger the compounding effect.
Interest Rate vs Compound Interest: The Rate and the Rule for Applying It
| Interest Rate | Compound Interest | |
|---|---|---|
| What it specifies | How much is charged or earned per period | Whether interest already earned starts earning too |
| Enough on its own to find a balance | No, the compounding frequency is still missing | No, it needs a rate to work on |
| Where it sits in a contract | The quoted percentage | The clause saying how often interest is added |
| Effect over the first period | Sets the whole amount | None, simple and compound agree after one period |
| Effect over long horizons | Understates growth if read as a flat annual figure | Widens the gap the longer the term runs |
| The figure that captures both | APR, which ignores compounding inside the year | APY, which folds the compounding in |
The quoted rate hides the frequency, which is why two acronyms exist
A rate quoted as 12 percent a year does not tell you what a year actually costs, because lenders usually charge monthly. Twelve percent nominal charged monthly means 1 percent added twelve times, and that raises a balance by about 12.68 percent over the year rather than 12. Those two figures are what the acronyms separate. The annual percentage rate states the periodic rate multiplied out and ignores compounding within the year. The annual percentage yield states what a full year actually does to the balance. Compounding more often keeps pushing the yield up but with sharply diminishing returns, because the ceiling at 12 percent nominal is continuous compounding, which gives about 12.75 percent. Monthly already captures all but roughly seven hundredths of a point of that maximum, so daily compounding is a marketing detail more than an economic one. The practical rule is that frequency matters a lot moving from annual to monthly and barely at all after that, and that two loans quoted on different frequencies must be compared on effective annual terms before either number means anything.
Run the same arithmetic backwards and you get present value
Compounding carries a sum forward. Discounting carries a sum back, using the identical formula rearranged. If 600 dollars grows to about 755.83 dollars in three years at 8 percent, then 755.83 dollars promised three years out is worth 600 dollars today at that rate, because dividing by 1.08 three times undoes multiplying by it. Everything that makes compounding powerful makes discounting severe in the other direction, since a higher rate or a longer wait shrinks present value fast. That is the bridge from this comparison to asset prices. A bond, a share and a factory are all claims on future cash, so raising the rate used to discount them lowers what they are worth today, which is the underlying reason asset values fall when rates rise. On an exam the giveaway phrase is worth today, which always means divide, as against accumulates to, which means multiply. Getting the direction right is usually worth more marks than getting the decimals right. Work either direction at /calculate/present-value or /calculate/compound-growth.
Frequently asked questions
What is the difference between an interest rate and compound interest?
The interest rate states the percentage charged or earned per period. Compound interest describes the rule that interest already earned is added to the balance and then earns in its turn. A rate needs the rule before it produces a number: 8 percent on 600 dollars for three years gives 744 dollars if the interest is simple and about 755.83 dollars if it compounds annually. Reading a contract properly means finding both the rate and the compounding frequency.
Is APR the same as APY?
APR and APY differ whenever interest compounds more than once a year. APR multiplies the periodic rate out and ignores compounding inside the year, so 1 percent a month is quoted as a 12 percent APR. APY folds the compounding in, and 1 percent added twelve times works out to about 12.68 percent. Comparing a loan quoted as an APR against one quoted as an APY makes the first look cheaper than it is.
How long does compound interest take to double your money?
Doubling time comes from the rule of 72: divide 72 by the annual rate. At 8 percent that predicts about nine years, and the exact calculation agrees, since 1.08 raised to the ninth power is 1.999. At 6 percent it predicts twelve years and at 3 percent about twenty-four, both of which check out. Simple interest is far slower, needing twelve and a half years to add 100 percent at that same 8 percent rate.
Live Loanable Funds graph. Drag the curves, or open the full version.
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