1 · One month of growth
A yearly rate has to be cut into twelve equal pieces that multiply back up to the year. Not division — the twelfth root.
Twelve of these multiplied together give exactly the yearly rate back.
Your assumptions
Five numbers. The contribution is paid on the first day of every month, so it earns growth from that month onwards.
Where every number comes from
Nothing below is hidden in a black box. These are the same formulas the table underneath is built from, with your numbers already filled in.
The formula renderer did not load, so the notation below is shown as plain text.
2 · The rule, every month
The contribution goes in first, then the whole balance grows. That is what “paid at the start of the month” means, and it is worth one extra month of growth on every contribution.
3 · The very first month
Your numbers, in that rule, for month one.
4 · Skipping to the end
Applying the rule 240 times in a row collapses into one line — the starting amount compounded, plus an annuity-due of the contributions.
The long way and the short way agree: this is the same figure as the last closing balance in the table. Past about a trillion rand the two can part by a cent — that is the computer's limit, not the arithmetic's.
5 · What it is worth in today's money
Inflation is not mixed into the monthly growth. It is applied once, at the end of each year, to that year's closing balance.
6 · Yours versus the growth
How much of the final figure you handed over yourself, and how much arrived on its own.
Step by step
Tap any row in the table below and this block follows it.
Year by year
Nothing is rounded on the way through. Balances are carried at full precision and rounded only where they are printed, so twelve months of growth land exactly on the yearly rate rather than a cent under it. Open a year to see the twelve months inside it.
Narrow screen — some columns are folded away to keep the table on the page. Tap any row for the full breakdown.
| Period | Opening (R) | Paid in (R) | Growth (R) | Closing (R) | Today's money (R) |
|---|---|---|---|---|---|
| Total |