Compounding: Interest That Earns Interest

Same $1,000, same 10% a year as last step. But now we change one rule: stop charging interest on the original $1,000 every time.

3 quick questions · about 2 min · no sign-up

Question 1 of 3

Simple interest always took 10% of the original $1,000 — a flat $100 every year. Compounding changes the base. Each year, what does the 10% get applied to instead?

• Still the original $1,000, every year
• The current balance, which grows each year
• The interest earned so far, not the principal
• I'm not sure

You said: Still the original $1,000, every year

That's the simple-interest rule from step 1. Compounding flips it: each year the 10% is applied to the current balance, not the original. After year 1 the balance is $1,100, so year 2's interest is 10% of $1,100 — not $1,000.

You said: The current balance, which grows each year

Exactly. The 10% rides on the new, larger balance every period. After year 1 you have $1,100, so year 2 charges 10% of $1,100 = $110 — and the balance you earned on keeps getting bigger.

You said: The interest earned so far, not the principal

Close, but it's the whole balance — principal plus interest together. After year 1 that's $1,100, so year 2's 10% applies to all $1,100, giving $110, not just to the $100 of interest.

You said: I'm not sure

No problem. The 10% applies to the current balance, which grows each year. After year 1 you have $1,100, so year 2's interest is 10% of $1,100 = $110 — bigger than last year because the base got bigger.

Another way to see it

Another way to see it: with simple interest your $100 of year-1 interest just sits there, earning nothing. Compounding lets that $100 join the principal and start earning its own 10% — so interest begins making interest.

So the base grows. Let's run year 2 and see what that does to the number.

Question 2 of 3

End of year 1 you have $1,100 either way. Under compounding, what's year 2's interest — and how does it compare to simple interest's flat $100?

• $100 — same as simple, the rate didn't change
• $110 — ten dollars more than simple
• $121 — the balance times 10% squared
• I'm not sure

You said: $100 — same as simple, the rate didn't change

The rate is the same, but the base isn't. Compounding charges 10% of the $1,100 balance, not the original $1,000 — that's $110, ten dollars more than simple's flat $100. That extra $10 is interest earned on last year's interest.

You said: $110 — ten dollars more than simple

Right. 10% of $1,100 is $110, versus simple interest's flat $100. That extra $10 is your year-1 interest now earning its own interest — the first crack where compound pulls ahead.

You said: $121 — the balance times 10% squared

You're anticipating where this heads, but for year 2 alone it's just 10% of the $1,100 balance = $110. ($121 is what year 3's interest becomes, once the base climbs to $1,210.)

You said: I'm not sure

It's $110. Year 2 charges 10% on the $1,100 balance, not the original $1,000 — so $110 versus simple's flat $100. The extra $10 is last year's interest now earning interest of its own.

That $10 gap looks tiny now. Push it one more year and watch the two paths separate.

Question 3 of 3

Carry it to the end of year 3. Simple interest sits at $1,300 ($100 × 3 added to $1,000). What's the compound balance?

• $1,300 — they end up the same after 3 years
• $1,331 — past simple's $1,300
• $1,310 — about $10 ahead of simple
• I'm not sure

You said: $1,300 — they end up the same after 3 years

Compound has already pulled ahead. Year 2 ended at $1,210, then year 3 adds 10% of $1,210 = $121, landing at $1,331 — $31 past simple's $1,300. The gap widens every year from here.

You said: $1,331 — past simple's $1,300

Exactly. $1,000 to $1,100 to $1,210 to $1,331 — each year's 10% rides a bigger base. You're $31 ahead of simple already, and that lead accelerates the longer you wait. That's the whole 'aha'.

You said: $1,310 — about $10 ahead of simple

Right direction, but bigger. Year 2 ends at $1,210, and year 3 adds 10% of that = $121, reaching $1,331 — $31 ahead, not $10. The gap itself grows because each year's base is larger.

You said: I'm not sure

It's $1,331. Track the balance: $1,000 to $1,100 to $1,210 to $1,331, multiplying by 1.10 each year. That's $31 past simple's $1,300 — and the gap keeps widening.

The takeaway

Compounding applies the rate to the growing balance, not the fixed principal — so interest starts earning interest. Same $1,000 at 10%: simple reaches $1,300 in three years, compound reaches $1,331, and the gap only widens from here.

Next step

Now that you've seen interest compound on a growing balance, the next step stretches that mechanic across many years to reveal its true shape and why starting early matters.