← all units · Unit 06 · Exponential functions
Compound interest
This is the one unit that will touch nearly every dollar you ever earn or borrow. The same rule that grows your savings is the one that grows your debt — so it's worth actually understanding.
Where you'll actually use this
Start investing at 22 instead of 32, and the same monthly deposit can be worth roughly twice as much by retirement. That gap is nothing but compounding.
A credit-card balance compounds too. At 24% APR, an unpaid $1,000 quietly becomes about $1,270 in a year — before you buy a single new thing.
The same exponential curve models populations, medicine in your bloodstream, and how fast a video spreads. Learn it once, recognize it everywhere.
The idea
Simple growth adds the same amount every step. Compound growth adds a percentage of the new total every step — so it grows on its own growth. That tiny difference is the whole game.
A = P (1 + r)t
- A
- amount you end with
- P
- principal — what you start with
- r
- rate per period, as a decimal
- t
- number of periods
Compounded more often than yearly? Split the rate and multiply the periods: A = P (1 + r/n)n·t.
Worked example $1,000 at 5% for 3 years: A = 1000(1.05)3 = 1000 × 1.157625 ≈ $1,157.63. The extra $7.63 over "just 15%" is the growth-on-growth.
Your turn
Fresh numbers every time. Miss one and you get the full worked solution — the point is to see the steps, not to be right on the first try.
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Snowball
Drag the sliders and watch it roll. Flip to debt to see the same curve turn into the thing that's chasing you.
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Next in this unit: simple vs. compound side by side, then solving for time. Connects back to arithmetic vs. geometric sequences.