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Simple vs. Compound Interest Explained
Simple interest is calculated on the original principal only. Compound interest is calculated on the principal plus all previously earned interest. That one difference produces very different results over time, and understanding which type applies to your loan or investment changes how you evaluate it.
The simple interest formula
\[I = P \times r \times t\]Where I is interest earned, P is the principal, r is the annual rate as a decimal, and t is time in years. The total after t years is A = P + I = P(1 + rt).
On $5,000 at 6% simple interest for 10 years, the interest is 5,000 x 0.06 x 10 = $3,000, for an estimated total of $8,000. You earn the same $300 every year because the calculation always uses the original $5,000, never the accumulated balance. Try it with the simple interest calculator.
A second example shows how the principal scales the result proportionally. On $20,000 at 4% simple interest for 5 years, the interest is 20,000 x 0.04 x 5 = $4,000, for an estimated total of $24,000. The annual interest payment is $800, every year, with no variation. That predictability is one reason simple interest appears in certain loan structures. The borrower and lender both know the exact cost from day one.
The compound interest formula
\[A = P\left(1 + \frac{r}{n}\right)^{nt}\]Where A is the estimated future value, P is the principal, r is the annual rate, n is the number of times interest compounds per year, and t is years.
That same $5,000 at 6% compounded annually for 10 years gives A = 5,000 x (1.06)^10 = approximately $8,954. The interest earned is approximately $3,954, which is $954 more than simple interest on the same terms. The extra comes from earning interest on interest. The compound interest calculator shows how this grows year by year.
Side-by-side comparison
| Year | Simple interest balance | Compound interest balance (annual) |
|---|---|---|
| 0 | $5,000 | $5,000 |
| 1 | $5,300 | $5,300 |
| 2 | $5,600 | $5,618 |
| 3 | $5,900 | $5,955 |
| 5 | $6,500 | $6,691 |
| 7 | $7,100 | $7,518 |
| 10 | $8,000 | $8,954 |
In year 1, both balances are $5,300 because there is no prior interest to compound yet. By year 10, the compound balance is approximately $954 ahead. Over 20 years, the gap widens further: simple interest on $5,000 at 6% yields $11,000 total, while compound interest yields approximately $16,036. At that point the compound balance is $5,036 ahead, more than the original principal itself.
The Rule of 72
The Rule of 72 is a quick shortcut for compound interest: divide 72 by the annual interest rate to estimate how long it takes to double your money.
| Interest rate | Approximate years to double |
|---|---|
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
Simple interest at 6% takes 16.7 years to double, because growth is linear rather than exponential. The Rule of 72 calculator does this math instantly. For a deeper look at how the Rule of 72 fits into compounding strategy, see how compound interest really works.
How compounding frequency changes results
More frequent compounding means interest gets added sooner, so it starts earning its own interest earlier. On $5,000 at 6% for 10 years:
| Compounding frequency | Estimated balance |
|---|---|
| Annually | $8,954 |
| Monthly | $9,097 |
| Daily | $9,110 |
The jump from annual to monthly adds approximately $143, but going from monthly to daily adds only $13. Returns diminish as frequency increases. The complete guide to compound interest covers how frequency, time, and contributions interact.
A common mistake: confusing APR and APY
Many people mix up APR (annual percentage rate) and APY (annual percentage yield). APR is the stated rate without accounting for compounding. APY includes the effect of compounding within the year. A savings account advertising 5.00% APY at daily compounding has an APR of approximately 4.88%. The difference matters when comparing products. A loan quoting 6% APR compounded monthly has an effective annual cost of approximately 6.17%. When comparing two financial products side by side, convert both to the same measure. APY gives the true annual return for savings, and effective annual rate gives the true annual cost for loans.
When each type applies
Simple interest is common in short-term personal loans, auto loans, and some bonds. When you take out a car loan, the interest is often calculated using simple amortization, though each payment recalculates interest on the remaining balance.
Compound interest is the standard for savings accounts, certificates of deposit, investment returns, and most long-term financial products. Credit card debt also compounds. A $5,000 credit card balance at 20% APR compounded daily grows to approximately $6,107 after one year if no payments are made. The same balance at simple interest would be $6,000. That $107 difference grows much larger over time if the balance is not paid down.
The distinction also matters when evaluating student loans. Federal student loans accrue simple interest while you are in school or during deferment. Once unpaid interest capitalizes (gets added to the principal), the loan effectively switches to compound interest on the new, larger balance. A $30,000 student loan at 5% that accrues $1,500 in simple interest during a one-year deferment becomes a $31,500 balance once that interest capitalizes. From that point forward, interest is calculated on $31,500 rather than $30,000.