## Concept explanation **Principal** is the starting amount of money you begin with, and **interest** is extra money added as a **percentage** of that starting amount. Because the percentage is taken from the starting amount, a larger principal produces more interest, while a smaller principal produces less. ## What you see The gold coin pile shows the starting money, and the smaller bouncing teal baby coins show the interest earned from it. As the starting pile grows, the interest pile grows too, helping you compare the original amount with the extra money it creates. ## Try it yourself - **Move the starting amount slider** and watch the gold pile get bigger or smaller. - **Notice the baby coins update at the same time** so you can see that more starting money creates more interest. - **Adjust the interest rate slider** to compare how a bigger percentage creates extra money faster. - **Watch the interest earned value** in the control panel and connect the number to the size of the baby-coin pile. - **Press Reset** to return to the original example and try again. ## Concept explanation **Compound interest** means each new round of growth is calculated from the **current total**, not just the starting amount. That means interest is earned on the original coins and also on coins that were added in earlier rounds. As the stack gets taller, the next layer can grow too, because the percentage is being applied to a bigger whole. ## What you see You’re looking at a coin stack where the gold layer is the starting amount and each colored layer above it is a new round of interest. The `Totals by round` card keeps track of how many coins are in the stack after each step, and the small preview card shows whether the newest added layer is bigger than the previous one. ## Try it yourself - **Click `Next round` once** and notice that a new smiling layer appears on top of the original stack. - **Click `Next round` several more times** and watch how the added layers often become larger, because the interest is being calculated on the updated total. - **Move the `Interest rate` slider** and then **press `Reset`** to start again with a different growth rate. - **Move the `Starting coins` slider** and **press `Reset`** to compare how a larger starting stack changes the later layers. - **Read the `Totals by round` panel after each click** to connect the growing stack with the changing total. ## Concept explanation With **simple interest**, you earn interest only on the original starting amount, so the total grows by the **same fixed amount** each period. With **compound interest**, each new period earns interest on the original amount **and** on earlier interest, so the increase gets larger over time. That is why simple interest makes a straight, steady pattern, while compound interest starts similarly but then speeds up. ## What you see You are watching two goofy racers on parallel tracks that represent money growing from the same starting value. The **simple** racer moves in equal jumps, showing that each period adds the same amount. The **compound** racer makes jumps that gradually widen, showing that each period adds more than the one before. The dots mark earlier stopping points, and the value tags let you compare how far each racer has grown after the selected number of periods. ## Try it yourself - **Drag the periods slider** slowly from `0` upward and notice how the simple racer advances by evenly spaced jumps. - **Keep dragging the slider** and watch the compound racer begin to pull ahead as each jump gets longer. - **Pause at a small number of periods** and compare the racers' value tags to see that the totals can start out close together. - **Move to a larger number of periods** and notice how the gap widens because compound growth accelerates. - **Press Reset** and then **scrub the slider again** to replay the race and focus on how one pattern is linear while the other curves upward in pace. ## Concept explanation When **compound interest** is paid more often, the money you earn gets added back into the balance sooner, so that new interest can start earning interest too. Over the same total number of years, **more frequent compounding** usually makes the final amount a little larger because each growth step gets reused earlier. ## What you see Each pot shows the same starting money growing into a cartoon money plant, but with a different compounding schedule: yearly, monthly, or daily. Taller plants and more coin sprouts represent a larger ending balance, so you can compare how the growth changes when interest is reused at different intervals across the same time span. ## Try it yourself - **Open the time-span dropdown** and switch between `1 year`, `3 years`, `5 years`, and `10 years` to compare the final plant heights. - **Watch which plant ends tallest** after each regrowth animation, and notice that the daily plant is usually slightly higher than the monthly one, which is slightly higher than the yearly one. - **Press `Replay growth`** to see the same time span animate again and focus on how the coin sprouts appear more densely on the more frequently compounded plants. - **Compare the dollar totals under each pot** and look for the small but consistent advantage created by compounding more often. - **Try a short span and then a long span** to see that the difference starts small but becomes more noticeable as time increases. ## Concept explanation **Compound growth** means your money grows not only from the original amount, but also from earlier growth that gets added back in again and again. That is why **time** is so powerful: each extra year gives the total more chances to compound, so later gains become much larger than early ones. At first the ride feels slow, but after enough years the curve bends upward and the growth starts to feel dramatic. ## What you see You are looking at a money-growth roller coaster. The little cart full of coins rides along the compound-growth curve, starting on a gentle slope and climbing onto a much steeper track as the years increase. The total amount card shows how much the money has grown so far, while the late-year boost card highlights how much extra growth comes from compounding rather than just simple steady increase. ## Try it yourself - **Drag the years slider** to move the cart forward and watch how the total changes only a little at first. - **Keep dragging into the later years** and notice how the same one-year step suddenly adds much more money. - **Drag the cart directly on the curve** to scrub through time and feel the coaster speed up. - **Adjust the rate slider** to compare a gentler hill with a much steeper late-stage climb. - **Press `Reset`** and then replay the motion, paying attention to how the early years look calm while the later years surge. ## Concept explanation When you save money, **compound interest** means you earn interest not only on your starting amount, but also on the interest that has already been added. If you also make **regular deposits**, each new contribution gets its own chance to grow too. That is why savings with repeated contributions can rise much faster than leaving the original amount alone: you are growing a bigger and bigger pile, and interest keeps working on the whole pile. ## What you see You are looking at a cartoon money monster whose belly is a transparent jar. As the animation plays, coins fall into the jar each month to represent your monthly deposit, while the jar total rises as interest is added. The graph compares two paths over the same time period: the teal line shows savings with deposits plus compounding, and the gold line shows what happens if the original amount is left alone to earn interest. ## Try it yourself - **Set the monthly deposit to `$0` and press `Play`** to see what interest alone does to the starting savings. - **Increase the monthly deposit and press `Play` again** to watch many more coins drop in and notice how much higher the teal path climbs. - **Keep the deposit the same, then raise the interest rate** and see how compounding makes both totals grow faster. - **Compare the difference readout in the control panel** to see how repeated contributions widen the gap over time. - **Use `Reset`, change one slider, and replay** so you can test which matters more: adding more each month or earning a higher rate.