Compound interest gets described as magic, which is unhelpful, because it stops people doing the arithmetic. The arithmetic is short and it settles most questions about long-term saving on its own.
This article explains how the maths works. It is not financial advice, and it does not recommend any particular investment.
The mechanism
Simple interest pays on your original amount. Compound interest pays on your original amount plus all the interest already earned. That single difference is the whole story.
Put in 1,000 at 8 percent:
- After 10 years: about 2,159
- After 20 years: about 4,661
- After 30 years: about 10,063
- After 40 years: about 21,725
Notice the shape. The second decade adds 2,500. The fourth adds 11,600 — more than four times as much, from the same original 1,000 and the same rate. The growth is not linear and this is why intuition fails here.
The rule of 72
Divide 72 by the annual rate and you get the approximate number of years for money to double. At 6 percent, twelve years. At 9 percent, eight years. At 12 percent, six.
It is accurate enough for mental arithmetic and it lets you answer real questions quickly. “If I leave this for thirty years at 8 percent, how many doublings?” Nine years per double, so a bit over three doublings, so roughly eight times the original.
Time beats rate — usually
Two savers, both investing 200 a month at 8 percent.
- Saver A starts at 22 and stops at 32. Ten years of contributions, 24,000 in total, then leaves it alone until 62.
- Saver B starts at 32 and contributes until 62. Thirty years of contributions, 72,000 in total.
At 62, Saver A has more, despite putting in a third as much. The ten years at the beginning were worth more than twenty extra years of contributions at the end, because every one of A’s early payments got four decades of compounding.
The practical implication is uncomfortable and clear: the amount matters much less than the start date. Small and early beats large and late.
The two things that undo it
Fees
A one percent annual fee does not cost you one percent. It costs you one percent compounded, every year, on the whole balance. Over forty years, a one-percent fee typically consumes something in the region of a quarter of the final value. This is why fee comparison is not a minor detail.
Inflation
An 8 percent return with 3 percent inflation is a 5 percent real return. Always do the comparison in real terms, because 8 percent sounds like it doubles your purchasing power in nine years and it actually takes about fourteen.
Compounding runs both ways
Debt compounds with exactly the same mechanism and usually at a higher rate. A credit card at 24 percent doubles what you owe in about three years if you pay nothing. No realistic investment return beats paying that off, which is why clearing high-interest debt sits ahead of investing in almost every framework you will read.
What to do with the arithmetic
Work out three numbers for yourself. How much can you set aside monthly without changing your life. How many years until you need it. What real return is plausible for the kind of holding you are considering. Then run the compound formula, or any online calculator, and look at the result.
Usually one of two things happens. Either the number is larger than you expected, which is motivating, or it is smaller, which tells you the plan needs a longer horizon or a bigger contribution. Both are useful. Neither is available if you never do the calculation.
If you want the same habit applied to your academic record, the target CGPA planner works on the same principle: state the goal, state the time remaining, and let the arithmetic tell you what the interval has to look like.