Here's a great way that has nothing to do with money but instead something tangible that's easier for young minds to grasp.

Plants!

What you want to do is get your hands on some heritage-grade seeds - the sort that will grow plants that then make their own seeds that will produce more plants. Some sort of beans might be a good choice, but look into various options and pick something that will be interesting for the whole family (ideally, something tasty).

Involve them in the process of sprouting, transplanting, and caring for the plants. Explain how you are investing water, soil nutrients, time, and energy (both directly from your own work, and indirectly through exposure to the sun) to help the plant grow and make more seeds. Then when it comes time to harvest those seeds, start the process again - but this time aim to grow several more plants. They can help with more of the work during this 2nd round as they'll have already gone through the process with you once.

If you have the space, you could also go with something really impacting like a fruit tree. You can get an idea of how long this takes (multiple years) from sites like this one:

https://www.starkbros.com/growing-guide/article/how-many-years

Over time, they'll get a valuable lesson in how setting constructive processes into play through disciplined application of inputs over the long-term can yield impressive results.

市場上有許多棋盤遊戲正是採用這種方式設計的。

這類游戲的總體思路是，您可以獲得積分（XP）和金錢。最後，分很重要-最終得分。 Money 僅在遊戲過程中很重要，您需要它來獲得XP，但這不是遊戲的目標。遊戲的運作方式通常是，一開始您幾乎沒有錢。如果您在遊戲開始時就將其用於XP，則會輸掉比賽。遊戲迫使您投入資金以獲得複合增長，然後您就可以開始花錢了。在支出和投資之間找到合適的平衡，就像在現實生活中一樣。

我的第一個想法是聖彼得堡（10+）， Agricola（ 12歲以上），輝煌（10歲以上），但還有很多其他遊戲，我相信您還會發現適合小孩子的東西。找到當地的桌遊俱樂部或好的桌遊經銷商，並向他們尋求建議。您可以先參加很多比賽，然後購買自己喜歡的東西。

如果他們可以算數，那麼可以快速輕鬆地對它們進行設置：

挑戰他們，將米粒放在國際象棋/跳棋/草稿板上的第一廣場。然後讓他們在第二個方塊上放置兩個，在下一個方塊上放置4個，在下一個方塊上放置8個，...他們很快就會意識到任務的不可能，並且將學習複利/成長非常強大！

這是一個眾所周知的問題。總顆粒數將達到18,000,000,000,000,000,000。

現在，他們已經看到了複合動力的增長，您可以使他們對這款遊戲更加有趣。正如瓦爾特克（Valthek）在評論中所建議的那樣，您可以通過設置兩塊木板來對抗它們，一個為您，一個為他們，以及百萬風格的甜蜜/糖果。然後，您可以在他們可能會吃掉甜食的同時發揮儲蓄/投資策略。為了使遊戲更加逼真，讓您的伴侶或其他中立的人扮演“銀行家”的角色，以使他們不認為您只是在付出額外的努力或製定規則。

Both Jeremy Jamesons and Joshs answers are good examples, each having their own advantages and disadvantages. We have a group activity, and a solo game. Allow me to offer a third choice which has its own different advantages and disadvantages, a 2 player competitive game.

The version I came up with uses Money, but you can use almost anything you have a lot of. Money just has several perks compared to most other times, such as the fact that they should know the inherent value and power of money.

How you play is simple, each person starts with a set amount, and each person gets a certain amount of money per turn. One gets a set number of money per turn, a linear amount, while the other gets a compound amount. The players then take turns getting their money until many rounds later when the compound is the clear winner.

A solid example (using American currency here):

You both start with 5 pennys(or one Nickel). The linear growth person gets 2 pennys per turn, while the Compound growth person gets 1 pennys per 5 they already have per turn (no fractions)(a more visually simply way to view that, one penny per Nickel).

Using those rules, the linear path starts off stronger, but after the 12th round, the compound pulls ahead by a penny, and the gap just gets wider from there.

Like this, if the child chose linear, they will likely feel the superior choice, easily beating the adult early on. This shows that the linear choice feels good early on, because in the short term, its better early on. After a while though, the Compound method catches up and then surpasses it, showing that its better in the long run.

There is an essays worth of things you can do or say to help the child understand why compound wins in the end, but that is far to long to really get into in the answer (maybe Ill throw some thoughts in the comments if needed/requested). There is also the issue that the linear player looses, and many children hate loosing, among other things.

There are two fundamental problems here.

Firstly, any demonstration of compound interest, if done right, starts to require inordinate amounts of the thing being compounded to be a valid and engaging demonstration. This leads to the temptation to use something meaningless or without value, say a grain of rice, which means you're asking them to not only learn the lesson but learn it by projecting value onto something that is not valuable to them. Most children engage better in lessons that involve something that they instinctively value to maintain their interest.

The second is that most benefits of compound interest occur over large time periods, which can make it difficult to maintain the coherence of the lesson or tempt teaching it quickly with a game, which might undermine the necessity of patience that is required to benefit from compound interest.

One of the better examples of compound growth is with fast-breeding animals. In one week, with one division per day, one thing multiplies to become 64 things. If you project this behaviour onto small valued items, say candies like jelly beans, the quantities involved aren't too excessive (maybe curb it down to 6 days to ensure a 32 maximum). Place the jelly beans in a number of Petri dishes and label them. Check on them once a day when a treat is appropriate and offer the opportunity to take/eat some, but not all, of them from each dish (at least one must remain to 'grow'). Encourage them to leave some of the dishes more full to 'grow faster', maybe set one dish aside for yourself to demonstrate the benefits of not withdrawing at all.

Each night, you multiply the treats appropriately and, each week, you reset the experiment to keep the numbers manageable... maybe by sharing/eating your dish! There's also potential to exploring sharing lessons (if one child ends up with a lot more than the others), or saving accounts (offer to seal a dish for a week and only let them look at it/add to it from their other dishes), and have other analogies for good financial practices (balancing income and outgoings, maybe exploring debt; jelly beans could 'die' and turn into raisins) later on as they grow up.

This should prevent overrun with the numbers involved, gives easy-to-understand contrast, persists the illustration over a long period of time without losing engagement, and is engaging and interesting on a value level. It also might back-door a little biology as well.

Video games, especially numbers-heavy games, often have exponential growth involved. If your kids enjoy video games and get to the point they thoroughly understand the strategies involved, they can understand compound interest.

For example, once your children are old enough, a grand strategy game like Civilization provides a powerful demonstration. These games have you manage a kingdom or empire with the goal of becoming the most powerful political state in the world. The winning strategy involves consistently investing and re-investing your resources into systems that allow you to gain more resources more quickly. If you become lazy about investing resources, spend them on investments that don't have good returns, or blow too many resources at once to be able to invest well in the future, you can quickly lose your ability to keep up with other kingdoms. But if you invest carefully and strategically, you can gain so much momentum that, by the end of the game, you are completely unstoppable.

The interesting thing is that the systems you use to gain more resources remain largely unchanged throughout the whole game. But as you build more cities and expand your empire, the same systems mean you gain more and more resources each turn - exponential, compound-like growth from simply having more video game money being invested and generating a return for you.

In the same way you need to continually reinvest your resources to grow more and more quickly in a grand strategy video game, you need to continually reinvest your money so that the same interest rate means your capital grows exponentially.

Compound growth is a great way for your kids to enjoy annoying their friends with long text messages.

For example, let's say you want to send your friend a flood of sunglasses emoji. You can type them one at a time:

Slow!

Or, you can repeatedly select-all, copy, paste:

Much faster!

Even though select-all, copy, paste feels like more work each step, you end up with a bigger flood of text in less time. With the power of compound growth, you can create unbelievably annoying texts and baffle your friends with how you can type so fast.

Simulate a savings bank with a 'piggy' bank where YOU (the parent) take on the role of the "bank".

This is pretty straightforward since we already teach kids to save their money with a piggy bank. You simply extend this to include compound interest returns where you act as the banker. This means that at the end of each month you and your child add up the balance, compute the interest, and you deposit that amount. To make this effective though, you ought to use a high interest rate (5% or greater) with a small principal balance and a small deposit for each month (or week if you choose).

Example:

Parent gives Child a piggy bank with a 5% monthly interest rate for 1 year. At the end of each month, Parent and Child get together and count the money saved. Parent teaches Child the algebra needed to compute the 5% interest. Parent deposits that sum into the piggy bank. Next month they do the same, but this time, if the balance wasn't spent, Parent may directly show Child that the 5% interest also applies to the 5% from the previous month. Over subsequent months, Child will see the long term effects of it. Once Child learns enough algebra, Parent may teach them the compound interest formula.

When I was in early elementary school I remember a children's book on this topic, "If You Made a Million". Might still be a little advanced for 2 and 4 year olds, but it was my first introduction to savings and compound interest. It may not be a demonstration per se, but could help reinforce the lesson.

It's actually a sequel to "How Much is a Million", which I also recall fondly. Indeed, in my memory they've run together, but this is probably more foundational and may be better for little ones.

Of course, it's a bit dated (80's/90's) and a million dollars (or pounds) isn't what it used to be (and savings accounts with over a percent interest!), but the concepts I think are generally still valid.

I believe the traditional way to introduce this topic (since 1256!) is by telling some version of the fable of the wheat and the chessboard:

Another version has the inventor of chess (in some tellings Sessa, an ancient Indian Minister) request his ruler give him wheat according to the wheat and chessboard problem. The ruler laughs it off as a meager prize for a brilliant invention, only to have court treasurers report the unexpectedly huge number of wheat grains would outstrip the ruler's resources. Versions differ as to whether the inventor becomes a high-ranking advisor or is executed.

For a toddler, you might suggest they try a few squares themselves, if you have some rice and a chess/checker-board to spare.^*

^{* - I'd also suggest telling the "high ranking advisor" variant, rather than the "executed" variant.}