The big ideaCompound interest pays on the interest already added, so growth speeds up.
How it works
Ana and Sam each planted 100 pretend coins. Sam's Flat Patch adds ten coins every year, the same each time.
Ana's Snowball Garden adds one coin for every ten inside, and counts the new coins too. Interest earns interest, so growth speeds up.
At first the snowball is small and slow, but later it races.
Ana's new coins each year. Sam gets ten every year.After ten years, the snowball is ahead.
Example 1: Sam's flat garden
Sam plants 100 and gets 10 coins a year.
After 5 years: 100 + 5 × 10 = 150
After 10 years: 100 + 10 × 10 = 200
Example 2: Ana's first years
Year 1: 100 holds ten tens, so 100 + 10 = 110.
Year 2: 110 holds eleven tens, so 110 + 11 = 121.
Year 3: 121 holds twelve tens, so 121 + 12 = 133.
Example 3: Why year three is special
Ana starts year three with 121 coins.
Ten new coins come from the planted hundred.
Two more come from the 21 interest coins.
10 + 2 = 12 new coins, so interest was earning interest!
Example 4: Who leads?
Year 3: Ana has 133 and Sam has 130, so 133 − 130 = 3.
Year 6: Ana has 176 and Sam has 160, so 176 − 160 = 16.
Year 10: Ana has 256 and Sam has 200, so 256 − 200 = 56.
The lead keeps speeding up.
Words to know
interest
The extra coins a garden adds.
simple interest
Interest paid only on the planted coins.
compound interest
Interest that earns its own interest.
snowball
It picks up more snow as it rolls, like compounding.
Watch out
Compounding starts slow. In year two Ana is only one coin ahead.
If Ana digs up each year's new coins, her garden stays at 100 and is flat, like Sam's.
Both gardens are good gardens. Compounding just grows faster the longer it runs.
These gardens are made up. Real ones pay different amounts, and nothing is promised.
Try it
Ana's garden holds 133 coins. How many new coins come next year?
Which garden pays on the interest coins too, the Flat Patch or the Snowball?
Sam plants 100 and gets 10 a year. How many coins after 5 years?
In year 10, Ana has 256 and Sam has 200. Who leads, and by how much?
Answers: 1. 13 coins · 2. The Snowball Garden · 3. 150 coins · 4. Ana, by 56 coins
Try at homeWith a grown-up, find something that grows faster as it gets bigger, like a snowball, a plant or a pile of folded paper. Talk about why.
For grown-upsLook for something at home that grows faster as it gets bigger, like a plant or a pile of folded paper, and talk about why. The gardens are made up and nothing real is promised: this is about how the idea works, not about what to do with money.
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