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Flip to reveal answersA compound-interest question gives PV, FV and the rate and asks for the number of years. What do you do?
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All 9 Flashcards — Compound interest
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Question
A compound-interest question gives PV, FV and the rate and asks for the number of years. What do you do?
Answer
Put them into FV = PV(1 + r/(100k))^(kn) and solve for n — take logs, or on Paper 2 scan the GDC table for when the balance first reaches FV. Spot which letter is the unknown before substituting.
Question
What does k stand for in the compound interest formula?
Answer
The number of compounding periods per year: annual k = 1, half-yearly 2, quarterly 4, monthly 12.
Question
How do you handle interest compounded more than once a year?
Answer
Divide the annual rate by k and raise to (k × n) periods: FV = PV(1 + r/(100k))^(kn).
Question
Find the value of $5000 at 4% compounded quarterly after 3 years.
Answer
5000(1 + 0.04/4)^(4×3) = 5000(1.01)¹² ≈ $5634.13.
Question
How is compound interest different from simple interest?
Answer
Compound multiplies the growing balance by (1 + rate) each period (geometric); simple adds a fixed amount each year (arithmetic).
Question
How can you compute compound interest on Paper 1 (no calculator)?
Answer
Write the one-year amount as PV(1 + x)⁴ for quarterly (the power = the number of periods in the year; x = the per-period rate), expand with the binomial theorem, and substitute the small x.
Question
Does more frequent compounding earn more?
Answer
Yes — for the same nominal rate, monthly beats quarterly beats annual, because interest compounds sooner.
Question
What is the interest earned, given FV and PV?
Answer
Interest = FV − PV (the growth above the amount invested).
Question
In FV = PV(1 + r/(100k))^(kn), what is the per-period multiplier?
Answer
1 + r/(100k) — one plus the per-period rate as a decimal.
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