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Flip to reveal answersHow do you model compound interest as a geometric sequence?
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All 8 Flashcards — Growth & decay
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Question
How do you model compound interest as a geometric sequence?
Answer
Each period the balance multiplies by r = 1 + (rate as a decimal). After n periods: balance = start × rⁿ.
Question
What is the common ratio for x% growth? For x% decay?
Answer
Growth: r = 1 + x/100. Decay: r = 1 − x/100. E.g. 6% growth → 1.06; 15% decay → 0.85.
Question
How do you find how long until an amount doubles?
Answer
Solve rⁿ = 2 (logs) or use the GDC/TVM solver; round n up to the next whole period.
Question
$2000 at 6% per year — when does it first exceed $4000?
Answer
2000 × 1.06ⁿ > 4000 → 1.06ⁿ > 2 → n ≈ 11.9 → 12 years.
Question
On the TI-84 TVM solver, how do you find the years to a target?
Answer
Enter I% = rate, PV = −start, PMT = 0, FV = target, P/Y = C/Y = periods per year, then solve for N. Money out is negative.
Question
How is depreciation different from growth?
Answer
Depreciation is decay: r = 1 − rate (0 < r < 1), so the value shrinks by a fixed percentage each period.
Question
Why is compound interest not the same as simple interest?
Answer
Compound multiplies the growing balance by r each period (geometric); simple adds a fixed amount each period (arithmetic).
Question
A machine worth $20 000 loses 15%/yr. Value after 4 years?
Answer
r = 0.85; 20 000 × 0.85⁴ ≈ $10 440.
Read the notes
Full study notes for Growth & decay
Topic 1.3 hub
Geometric sequences & series
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Math AA SL exam skills
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