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Retap · Examining: Compound Interest

Retap AI

You said compound interest "grows faster over time". Why exactly — what's the mechanism that makes it accelerate?

You

Because the interest gets added to the principal, so next time you earn interest on more?

Retap AI

Right. So if the rate doubles vs. the time doubles — which has a bigger effect on the final amount, and why?

Rate vs. time tradeoff · Gap detected

Sound familiar?

The illusion of understanding.

Most learning creates the feeling of knowing — not the thing itself.

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You use it every day.

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You passed the test.

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Here's what one session on a single topic looks like end-to-end.

AI Examination

Compound Interest

Retap AI

Let's examine your understanding of compound interest. In your own words — what makes it different from simple interest?

With compound interest, you earn interest on the interest you've already earned, not just the original amount.

Retap AI

Good. So why does it accelerate over time? What's the actual mechanism — not the effect, the cause.

Because the base keeps growing, so the same rate applies to a larger amount each period.

Retap AI

Exactly. Now — if you double the interest rate vs. double the time period, which has a bigger impact on the final amount? And why?

I think… doubling the rate? Because it compounds more each period?

Retap AI

It depends on the timeframe. For short periods, rate wins. For long periods, time dominates because compounding is exponential. Can you explain why time creates an exponential curve while rate doesn't?

Because the number of compounding periods grows… and each one multiplies the total?

Retap AI

Close. The exponent in the formula is the number of periods — so time literally changes the power. Rate changes the base. That's why time is the lever most people underestimate.

✓ Interest on interest — Strong✗ Rate vs. time tradeoff — Gap

Knowledge Map

Compound Interest

Your understanding, mapped

Interest on intereststrong

Simple vs. compoundstrong

Compounding frequencyweak

Rate vs. time tradeoffgap

Exponential curvegap

Inflation adjustmentgap

Real-world applicationweak

strong

weak

gap

AI-checked Flashcards

Compound Interest

Rate vs. time tradeoff · GapCard 1 of 4

Question

If the interest rate doubles vs. the time period doubles — which has a bigger effect on the final amount, and why?

Your answer

Doubling the rate has a bigger effect because the interest earned each period is larger, which then compounds further. Time just adds more periods but each period earns the same amount.

Retap AI · Feedback

Partially correct. You're right that rate increases each period's earnings — but your second sentence is wrong. Time doesn't just "add periods at the same rate": it changes the exponent in the formula, which is why its effect is exponential, not linear. For long horizons, time actually dominates over rate. Try rephrasing that part.

Accuracy: Partial

·Next review: in 2 days

Progress after spaced re-testing

Compound Interest

Before session

34%

After session

71%

Interest on interest70% → 95%

Simple vs. compound60% → 90%

Compounding frequency25% → 70%

Rate vs. time tradeoff10% → 58%

Inflation adjustment5% → 42%

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