Turning 10,000 into 15,000 is a 50 per cent return, and over three years that annualises to 14.5 per cent a year. A different investment returning 30 per cent over one year is better despite the smaller headline, and the only way to see that is to put both on the same annual basis before comparing them.
The same discipline applies to interest. Ten thousand at 5 per cent simple for five years earns 2,500; the same money compounding annually earns 2,762. The difference is interest on interest, and it grows non-linearly with both time and rate.
How does simple interest differ from compound?
Simple interest is principal × rate × time and pays only on the original amount. Compound pays on the accumulated balance, so the gap opens slowly and then widens.
| Years at 5% on 10,000 | Simple | Compound | Gap |
|---|---|---|---|
| 1 | 500 | 500 | 0 |
| 5 | 2,500 | 2,763 | 263 |
| 10 | 5,000 | 6,289 | 1,289 |
| 20 | 10,000 | 16,533 | 6,533 |
Over one year there is no difference at all, which is why the distinction feels academic until it is not. Over twenty years the compound figure is 65 per cent larger.
Simple interest still appears in the real world — some bonds, some short-term lending and many legal interest calculations use it — so it is worth knowing which one a quoted rate refers to before assuming the more generous reading.
What does CAGR actually describe?
The constant rate that would have produced the same two endpoints. Ten thousand growing to eighteen thousand over six years is a CAGR of 10.29 per cent a year, which at that rate would double every 7.08 years.
It describes a smooth path that almost never happened, and that is both its strength and its limitation. It is excellent for comparison, because it collapses any sequence of ups and downs into one comparable number, and misleading as a description, because it hides everything about volatility along the way.
Two investments with identical CAGRs can have had wildly different experiences, and the one that halved in year three was a much harder thing to hold.
The doubling rule follows directly. At 10.29 per cent a year, money doubles every 7.08 years, and the rule of 72 approximates that as 7.00 — close enough to do in your head and worth knowing is an approximation rather than the formula.
What does simple ROI ignore?
Two things that usually matter. The first is timing: money returned early can be reinvested, which is why internal rate of return exists as a more rigorous measure for uneven cash flows.
The second is what else the money could have done. A 14.5 per cent annualised return is excellent against a savings account and unremarkable against a period when the whole market rose 20 per cent a year — and ROI on its own has no way to say which.
The practical fix is to state the period, annualise it, and name the benchmark. All three take one line and remove almost every misleading comparison.
Is a high dividend yield a good sign?
As often a warning as an opportunity. Yield is the dividend divided by the price, so it rises when the price falls — and a price falling because the market expects a dividend cut produces a high yield that is about to disappear.
Five hundred shares paying 0.55 quarterly is 1,100 a year, which on a 42 share price is a 5.24 per cent yield. Whether that is attractive depends on whether the payment is sustainable, which the yield figure alone cannot tell you.
The figures worth pairing it with are the payout ratio — what share of earnings the dividend consumes — and the history of the payment. A yield that has risen sharply without the dividend rising is a price signal rather than an income one.
Questions people ask
Does a longer period always look better? Only in raw terms. A total return grows with time whatever the rate, which is exactly why comparing a five-year total against a one-year total tells you about the holding period rather than the investment.
How do I annualise a return? Raise the total growth factor to one over the number of years, then subtract one. A 50 per cent gain over three years is 1.5^(1/3) − 1 = 14.5 per cent.
Is CAGR the same as average annual return? No, and the difference matters. An arithmetic average of yearly returns overstates the outcome whenever the returns vary, because losses take a larger proportional gain to recover.
Should ROI include costs? All of them, including fees, tax where it applies, and the cost of any time invested. An ROI calculated on gross proceeds is a marketing figure rather than a measurement.
Does the rule of 72 still work? As an approximation, well. Dividing 72 by the rate gives the doubling time to within a few per cent across ordinary rates — 72 ÷ 10.29 gives 7.00 years against a true 7.08.
What about inflation? Every figure above is nominal. A 10.29 per cent nominal return during a period of 3 per cent inflation is about 7.1 per cent real, and it is the real figure that describes what the money will buy.
Annualise first, name the benchmark, and check what the yield is telling you. The simple interest calculator shows the gap against compounding, the CAGR calculator collapses a period into one rate, the ROI calculator annualises a total return, and the dividend calculator works income and yield in both directions.