When will I have enough?

How many months a target takes to reach at the amount you put aside each month, how much of it comes out of your own pocket, and how much the return adds. It sizes nothing for you — the target is yours, and nothing here checks it, and and it knows about one goal at a time, not the others competing for the same money.

• The return shortens the wait. What it added is above, and it is what you do not have to save.

Adding 3,000 a month to the 20,000 you hold reaches 200,000 in 54 months. By then you will have put in 182,000, and the return will have added 19,110 on top, with the target fixed in today's money.

The balance is run a month at a time. Each month it earns a twelfth of the annual return and the deposit is added at the end, which is what a standing order does; the count stops the first month the balance reaches the target. Adding at the start of each month instead would give every deposit one more month of growth and shorten the wait a little, and the difference grows with the return.

The split under the figure follows the compound interest calculator's exactly: what you put in is the balance you started with plus every deposit made since, and the growth is the rest. Splitting it the other way — the deposits alone against everything else — would put two meanings of one word on two savings pages, so it is not done.

Three states have no arrival month, and they are kept apart because the reasons are not the same. Nothing added and no return leaves the balance where it is, forever. A negative return that takes more each month than the deposit adds makes the balance fall, so the distance to the target grows rather than closes. And a balance that climbs every month can still be short of the target after a hundred years, which is not a failure of the deposits but a fact about the size of the target. Each of the three prints its own sentence; a single one would be false on two of them, and the false version tells a reader adding money every month that nothing is being added.

each month, balance = balance × (1 + rate ÷ 12) + what you add

The count stops the first month the balance reaches the target. What you put in is the balance you started with plus every deposit; the rest of it is the return.

A worked example

Saving 3,000 a month toward 200,000, starting from 20,000 already held, at 4% a year, the target arrives in 54 months. By then 182,000 has come out of your own pocket and the return has added 19,110 on top of it.

What it assumes

• The target is a fixed figure in today's money. Where prices are rising quickly the thing being saved for is not standing still, and a target set four years ago is not the target now.
• The deposit lands at the end of each month and is made every month without interruption. A month missed moves the arrival by more than that month, because there is nothing compounding to make it up.
• The return is the same in every year and compounds monthly. No real product does either, and a bad year early costs more than the same year late.
• Nothing is withdrawn along the way. A balance drawn on part way through arrives later than this by more than the amount taken out.
• Tax and charges are not part of this arithmetic. Where either applies it comes off the return before any of this starts, so the figure that belongs in the box is the return that reaches the balance.