Compound Interest vs Simple Interest
The difference between simple and compound interest, worked through with the same numbers, and why the gap widens the longer money stays put.
Simple interest and compound interest are the same idea computed two different ways, and the difference between them is one of the largest gaps in ordinary arithmetic.
Simple interest charges interest on the original amount. Compound interest charges interest on the original amount plus the interest already credited. That is the whole difference.
The same numbers, two answers
Take $10,000 at 7 percent over 30 years.
Simple interest pays 7 percent of the original $10,000 every year: $700 a year, unchanged, for thirty years. The final balance is $31,000.
Compound interest, compounded annually, starts at $10,000 and grows. The final balance is $76,123.
The gap is $45,123 on a $10,000 starting balance, and it comes entirely from the fact that compound interest is charged on a growing base.
The compound interest calculator runs the second case. To see the first, set the rate to zero and note that the balance then grows by the deposits alone — the simple-interest case is the same projection with the interest switched off.
Why the gap widens rather than stays constant
The growth is not linear. In a simple-interest account, each year adds the same amount. In a compound-interest account, each year adds slightly more than the year before, because the base has grown.
Three effects are worth separating, because they behave differently:
The interest on interest. The largest effect, and the one that requires the longest time to become significant. Over a year it is barely visible; over thirty years it is most of the balance.
The contribution effect. A regular monthly contribution is itself a form of compounding, because each contribution earns interest for the rest of the period. The contribution made in month one earns interest for the whole horizon; the one made in the last month earns almost none. This is why the tool lets you switch the contribution between the start and the end of the month.
The frequency effect. Same nominal rate, more frequent compounding, more money. The effective annual rate is what makes this visible: 7 percent compounded monthly is 7.229 percent, and 7.229 percent is the rate you are actually earning.
The doubling approximation
The rule of 70 is a shortcut: divide 70 by the annual rate to get the years it takes for money to double. At 7 percent that is ten years; at 3 percent, 23 years.
It is an approximation, and the reason it is needed at all is that the exact doubling time depends on the compounding frequency. The rule of 70 assumes annual compounding. With monthly compounding, 7 percent doubles a little sooner than ten years.
The calculator is the way to check it. Run thirty years at 7 percent with no contributions, and compare the final balance with twice the starting balance. The approximation is close; the exact figure is on the screen.
Where the same mechanism runs the other way
Compound interest is not a favour granted by finance. It is a property of the arithmetic, and it applies to balances owed as well as balances earned.
On a revolving credit card balance, the interest is charged on the balance including previous interest. Paying only the minimum on a card is the compound interest calculation running in reverse, with a rate that is high enough to make the effect quick.
The same is true of unpaid interest on some other arrangements. What determines the direction is only which side of the balance you are on.
A note on the rates involved
The Federal Reserve publishes the H.15 selected interest rates, which is the reference series for what savings products have actually paid. The Internal Revenue Service publishes the rules for the accounts where growth is deferred, and the Investor.gov glossary defines the terms used here.
None of those is a forecast of what a rate will be. The calculator uses whatever rate you enter, held constant for the whole horizon, because a projection that changes the rate according to some assumed future path is a different kind of claim from arithmetic.
Sources
These are the primary sources behind the figures and the method in this guide.
Calculators behind this guide
Common questions
What is simple interest?
Interest calculated on the original principal only, at the original rate, for the whole period. It does not grow: a $10,000 balance at 5 percent simple earns $500 a year for as long as it stays there.
What is compound interest?
Interest calculated on the balance, which includes interest already credited. Each period's interest is charged on a slightly larger base than the last, so the growth is not linear.
How big is the difference?
On a short horizon it is small. On $10,000 at 7 percent over 30 years, simple interest gives $31,000 and compound interest gives $76,123. The gap is the entire argument for leaving money alone.
Where do I actually meet simple interest?
Short-term consumer loans often use it, and some older savings arrangements did. It is also the mental model most people have, which is part of why compound interest is surprising.
Does compound interest work against me anywhere?
On credit cards and other revolving balances, where the interest is charged on the balance including previous interest. The same mechanism that works in your favour works in reverse.
Is the doubling rule reliable?
The rule of 70 is a useful approximation: divide 70 by the annual rate to get the years to double. At 7 percent that is about ten years. The calculator shows the actual figure rather than the approximation.