Simple interest pays you only on the money you put in. Compound interest pays you on that money and on earlier interest. At first the difference is a rounding error. Given enough time, it becomes most of the total.
The parts of the calculation
Principal is the amount already there. If you open with R5 000, that is the principal.
Contributions are the new amounts you add. A monthly debit order is a contribution, and each payment gets its own amount of time to grow.
Interest or return is the change applied to the balance. A savings account may describe it as interest. An investment may describe gains or losses as a return. A positive return is never guaranteed merely because a calculator accepts one.
Compounding means the next period starts with the previous period’s growth still in the balance. Nothing magical appeared. The base being multiplied simply got bigger.
One quiet line of maths
New balance = old balance × (1 + rate)
R1 000 growing by 10% becomes R1 100. Another 10% is then R110, not R100, because it is applied to R1 100. The second year ends at R1 210.
Monthly versus annual compounding
A rate needs a convention. “12% a year, compounded monthly” can mean a nominal 12% divided into twelve 1% months, which produces an effective annual result slightly above 12%. Or 12% can be an effective annual rate that is converted into twelve equal monthly factors which multiply back to exactly 12%.
Those are not the same calculation. Neither label is enough on its own; the convention matters. The My Money Matters calculator treats the number entered as an effective annual return, takes its twelfth root, adds contributions at the start of each month and carries full precision until a result is printed.
A future rand is still a rand, but it may buy less
Nominal value is the future number on the statement. Real value adjusts that number for assumed inflation so it can be compared with today’s buying power.
If a balance grows by 8% while prices rise by 5%, the real improvement is much closer to 3% than 8%. Over forty years, the gap between nominal and real becomes enormous. This does not make the nominal total false. It answers a different question.
What R500 a month looks like on a tidy calculator
Illustration only: 9% a year for 40 years
Start at R0. Add R500 on the first day of every month. Assume a steady 9% effective annual return, compounded through equivalent monthly factors.
| Your contributions | R240 000 |
|---|---|
| Modelled growth | About R1 884 824 |
| Nominal final value | About R2 124 824 |
| At assumed 5% inflation | About R301 822 in today’s money |
The return does not arrive smoothly in real life, and fees and tax are not separately deducted here. These are the results of assumptions, not predictions of an investment product.
Starting early versus starting later
Using the same R500 and 9% illustration, forty years produces about R2.12 million. Waiting ten years and then contributing for thirty produces about R857 000.
The early starter contributes only R60 000 more: R240 000 instead of R180 000. Yet the modelled final difference is about R1.27 million because those first contributions have ten extra years in which earlier growth can earn later growth.
This is not an instruction to accept any investment today. It explains why time is a powerful input and why a modest contribution started now can matter more than a heroic contribution repeatedly postponed.
The Rule of 72
Divide 72 by an annual percentage to estimate how many years it takes an amount to double. At 8%, 72 ÷ 8 gives roughly nine years. It is a mental shortcut, not an exact formula, and works best for ordinary positive rates.
The same shortcut can describe inflation working in the other direction. At 6% inflation, the general price level would roughly double in twelve years if that rate stayed constant. That is why real value belongs beside a long-term nominal number.
The result is only as honest as the assumptions
- Returns: actual returns are uneven, can be negative and are not guaranteed.
- Fees: recurring fees reduce the amount left to compound. A one-point difference repeated for decades is not small.
- Tax: the tax treatment depends on the account, investment, transactions and your circumstances.
- Inflation: future inflation is unknown, so a real-value calculation is another scenario.
- Contributions: real people pause, increase and withdraw money. A fixed monthly line is a model.
- Sequence: the order of gains and losses can matter greatly, especially when withdrawals begin.
Change one assumption at a time
Use the growth calculator to see the monthly arithmetic, compare contributions with growth and translate the final number into today’s money.
Open the investment growth calculator →