Guide Personal finance
Compound interest: what it is, and how long it takes to matter
Interest that stays in the account earns interest of its own, so what it pays grows every year without you adding anything. The useful part of knowing that is how long it takes to be worth something.
By NOUQUD Editorial Room3 min readUpdated
What compound interest is
Interest that stays in the account earns interest of its own.
Put 10,000 into an account paying 8% a year. The first year earns 800. The second year the 8% is applied to 10,800 rather than to 10,000, so it earns 864. Nothing about the rate changed. The number it is applied to did.
What compound interest is Plays on its own
You put 10,000 into an account paying 8% a year.
In the first year the 8% is applied to the 10,000, so it earns 800. The balance is now 10,800.
The 800 stays in the account, so what the second year's 8% is applied to is 10,800, not 10,000. The bracket is the definition.
So the second year earns 864, which is 64 more than the first. That is compound interest: the interest joins the base, the base grows, and so does what it earns.
- TODAY
- 10,000.
- YEAR 1 EARNINGS
- 800.
- YEAR 2 EARNINGS
- 864.
That is the entire mechanism, and it has one condition attached to it. If the interest is paid into your current account and you spend it, the base never grows, and none of this happens.
What makes it different from simple interest
Simple interest is always applied to the original sum, so it pays the same amount every year for ever.
At 8% that is 800 in the twentieth year exactly as in the first.
Compound against simple, over twenty years Plays on its own
Simple interest pays the same 800 every year, because it is always applied to the original 10,000. A straight line.
Compounding is applied to the balance as it stands. After ten years: 21,589 against 18,000. The gap is 3,589, which is smaller than most people expect.
After twenty: 46,610 against 26,000.
The whole of the difference is that the interest stayed where it was paid. Same rate, same sum. What changed is that the interest joined the base instead of being taken out.
- SIMPLE
- 8% of the original sum, every year, unchanged: 800 in the twentieth year exactly as in the first.
- COMPOUND
- The same rate applied to the balance as it stands, so the interest earns interest of its own.
Look at the ten-year mark before the twenty-year one. At ten years the gap is 3,589 on a 10,000 deposit, which is real but modest. At twenty it is 20,610. Compounding is not fast. It is relentless, which is a different thing, and the difference between those two words is most of what people get wrong about it.
When it has earned more than you put in
At 8%, the account has earned more than you put into it in year ten.
When what it earns passes what you put in Plays on its own
The dashed line is the 10,000 you put in. The curve is everything the account has earned since it opened.
After five years it has earned 4,693. Less than half of what you put in.
In year 10 what it has earned passes what you put in: 11,589 against 10,000. That is the year your money has doubled.
A shortcut worth knowing: divide 72 by the rate. 72 ÷ 8 = 9, and the true answer is 10. Close enough to think with, and wrong enough to sign nothing on.
- WHAT IT HAS EARNED
- Every unit of interest since the account opened. It bends because each year is applied to a larger balance.
That is the moment the balance has doubled, and it is worth knowing where it falls before making a plan that depends on it. Five years in, the account has earned 4,693, which is less than half the deposit.
The shortcut is worth learning: divide TermRule of 72قاعدة 72A quick way to estimate how many years it takes money to double at a given annual return rate.Open the term by the rate and you have roughly the years to double. Seventy-two over eight is nine, against a true answer of ten. Close enough to think with, and wrong enough to sign nothing on.
What moves the result
The rate and the time both move it, and the time moves it further.
The time and the rate, on one axis Plays on its own
Ten thousand at 8%, with nothing added. After ten years, 21,589, so the account has earned 11,589.
Ten more years at the same rate. The balance is 46,610, and the second decade on its own added 25,020, more than twice what the first one did.
A third decade: 100,627. That decade alone added 54,017, more than the two before it put together.
Now raise the rate to 12% and leave the money only 20 years: 96,463. Thirty years at 8% beats it. A bank sets the rate. You set the time.
- AT 8%
- The same sum left for thirty years. Every decade adds more than the one before it.
- AT 12%
- The same sum at a higher rate, but left for only twenty years.
Each decade adds more than the one before it. The first ten years earn 11,589, the second ten earn 25,020, and the third earn 54,017 on their own. Nothing about the account changed. It simply had more to work on each time.
That is why thirty years at 8% ends above twenty years at 12%, even though nobody would turn down the higher rate. A bank sets the rate. You set how long you leave it.
Two things this assumes. A rate held for thirty years is an assumption, not a plan, and an introductory rate is not a term rate. And every number here counts currency units, not what they buy: a balance growing at 8% in a year when prices rise 25% is getting larger and buying less. That is what TermInflationالتضخّمA general rise in prices over time, so one riyal today buys less than it did a year ago.Open the term is, and then what your savings rate is really paying, and both are guides of their own.
It works in both directions
The same arithmetic runs on what you owe, and there the rate is several times larger.
The same sum, pointed both ways Plays on its own
Ten thousand, twice. One in an account paying 8% a year. One on a card charging 2.5% a month.
After one year the saving has made 800 and the debt has added 3,449.
Year two: 1,664 above the line, 8,087 below it.
Year three: 2,597 above, 14,325 below.
The same machine, pointed at you. What differs is the rate: 2.5% a month is 34.5% a year, and it costs you 5.5 times what the saving earns.
- SAVED · 8% A YEAR
- The same account you watched above, in its first three years.
- OWED · 2.5% A MONTH
- 2.5% a month on the balance, with nothing paid off.
Nothing changes at the sign. A card at 2.5% a month is 34.5% a year, and over three years it takes 14,325 out of you while the savings account was earning 2,597. Which is why, of the two rates in your life, the one worth pricing first is the one you are paying.
Common questions
What is compound interest, in one sentence?
What is the difference between compound and simple interest?
How long before the interest is worth more than what I put in?
Does a higher rate or a longer time matter more?
Does the same thing happen to what I owe?
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