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Simple vs Compound Interest: How to Calculate Both
Simple interest is charged on the original amount only. Compound interest is charged on the balance, including interest already added. Over a few years the gap becomes large enough to change decisions.
The difference is what the interest is calculated on. Simple interest always uses the original principal, so every period adds the same amount. Compound interest uses the current balance, so each period's interest is slightly larger than the last. Over one year the two are close. Over ten years they are not.
The two formulas
In the compound formula, n is how often interest is added to the balance: 1 for annual, 12 for monthly, 365 for daily. The more often it is added, the sooner that interest starts earning interest itself.
Simple interest: A = P x (1 + r x t) Compound interest: A = P x (1 + r/n)^(n x t) P = principal, r = annual rate as a decimal, t = years, n = compounding periods per year
Worked example: the same deposit, both ways
Put 10,000 away at 6% a year for 10 years.
Under simple interest: 10,000 x (1 + 0.06 x 10) = 10,000 x 1.60 = 16,000. You earn 600 every year, ten times.
Under compound interest with annual compounding: 10,000 x (1.06)^10 = 17,908. The extra 1,908 is interest that was itself earning interest.
In year one both pay 600. In year ten, simple interest still pays 600 while compound interest pays about 1,014, because it is charging 6% on a balance that has grown to nearly 17,000.
How compounding frequency changes the answer
Two things are worth noticing. Frequency does help, and the step from annual to monthly is worth a few hundred over a decade. But the gains shrink quickly: going from monthly to daily adds around 27 on a 10,000 deposit across ten years. Frequency is a real factor and a poor reason to choose one account over another if the headline rates differ at all.
| Compounded | Periods per year | Balance after 10 years on 10,000 at 6% |
|---|---|---|
| Annually | 1 | 17,908 |
| Quarterly | 4 | 18,140 |
| Monthly | 12 | 18,194 |
| Daily | 365 | 18,221 |
Where each one actually applies
The direction matters as much as the mechanism. Compounding on savings works for you. Compounding on a credit card balance you are not clearing works against you at a much higher rate, which is why a 22% card is a more urgent problem than a 6% savings account is an opportunity.
- Simple interest: many short-term personal loans, some car finance structures, certain bonds that pay interest out rather than reinvesting it, and most late-payment penalties.
- Compound interest: savings accounts, most deposit products, credit card balances, and any investment where returns are reinvested rather than withdrawn.
- Mortgages and most instalment loans sit in between in practice. Interest compounds on the outstanding balance, but because you are also making regular payments that reduce that balance, the balance falls rather than grows.
A rough shortcut for doubling time
The rule of 72 estimates how long a compounding balance takes to double: divide 72 by the annual percentage rate. At 6%, that is 72 / 6 = 12 years. The exact figure, from the compound formula, is 11.9 years.
It stays reasonably accurate between roughly 4% and 12% and drifts at the extremes. It is a sanity check, not a calculation — useful for spotting when a projection you have been shown is implausible.
Mistakes that distort interest comparisons
- Comparing a simple-interest quote to a compound-interest quote as if the headline rates were equivalent. They are not; convert both to the same basis first.
- Using the annual rate without dividing by n. At 6% compounded monthly, each month uses 0.5%, not 6%.
- Forgetting that deposits and withdrawals during the period break the simple formula entirely. Regular contributions need a future-value-of-an-annuity calculation instead.
- Ignoring tax on interest. In many places interest is taxable, and the after-tax rate is what actually compounds.
- Treating a historical average return as a guaranteed compounding rate when projecting investments.
Assumptions and limitations
Both formulas assume the rate stays fixed for the whole period. Very few real accounts work that way. Savings rates are usually variable, promotional rates expire, and loan rates may be tied to a reference rate that moves. Running the calculation at two or three different rates shows you how sensitive the outcome is, which is more useful than a single precise-looking number.
They also assume no fees, no withdrawals and no additional deposits. An account charging a monthly fee can easily wipe out the advantage of a slightly better rate on a small balance.
And for investments rather than deposits, there is no fixed rate at all. Applying a compound formula to an assumed average return produces a projection, not a prediction — real returns arrive unevenly, and the order in which good and bad years land affects the outcome when you are also paying money in or taking it out.
Keep the compounding period consistent
A fair comparison uses the same principal, rate basis, time period and compounding convention for both methods. Simple interest grows from the original principal only; compound interest also earns on previously accumulated interest. If a quoted rate uses a different compounding period, convert the rates or model each schedule explicitly before comparing them.
Frequently asked questions
Which is better for a borrower?
Simple interest, all else being equal, because the interest charge does not grow on itself. In practice the rate and the fees usually matter more than which mechanism is used.
Does compound interest work on money I keep adding?
Yes, but the plain formula does not cover it. Each contribution compounds only from the date it arrives, so regular saving needs the future value of an annuity formula, or a savings calculator that handles recurring deposits.
What does 'compounded continuously' mean?
It is the mathematical limit of compounding infinitely often, calculated as A = P x e^(rt). It is used in financial modelling and produces a figure only marginally above daily compounding.
Is the rate on my savings account simple or compound?
Almost always compound, but check how often interest is credited and whether the advertised figure is the nominal rate or the effective annual rate, since those describe the same account differently.
When is simple interest commonly used?
It can be used in straightforward educational examples and some short-term agreements. The actual contract determines which method applies.
Does more frequent compounding always produce a much larger result?
It increases the compound result when the stated nominal rate is held constant, but the size of the difference depends on the rate, period and compounding frequency.
Conclusion
Simple interest grows in a straight line and compound interest grows in a curve, and the curve only becomes visibly steeper after several years. When you are comparing products, convert everything to the same basis before looking at the numbers, check how often interest is credited, and test the result at a rate a point or two lower than quoted — a projection that only works at the best-case rate is telling you something useful about how much risk is built into it.
Figures in this article are illustrative. Results depend on your own rates, fees, taxes and circumstances, and are for educational and planning purposes rather than financial advice.