Financial applications
Practice Flashcards
A 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 Flashcards in Topic 1.4
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1.4.19 cards
A compound-interest question gives PV, FV and the rate and asks for the number of years. What do you do?
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.
What does k stand for in the compound interest formula?
The number of compounding periods per year: annual k = 1, half-yearly 2, quarterly 4, monthly 12.
How do you handle interest compounded more than once a year?
Divide the annual rate by k and raise to (k × n) periods: FV = PV(1 + r/(100k))^(kn).
Find the value of $5000 at 4% compounded quarterly after 3 years.
5000(1 + 0.04/4)^(4×3) = 5000(1.01)¹² ≈ $5634.13.
How is compound interest different from simple interest?
Compound multiplies the growing balance by (1 + rate) each period (geometric); simple adds a fixed amount each year (arithmetic).
How can you compute compound interest on Paper 1 (no calculator)?
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.
Does more frequent compounding earn more?
Yes — for the same nominal rate, monthly beats quarterly beats annual, because interest compounds sooner.
What is the interest earned, given FV and PV?
Interest = FV − PV (the growth above the amount invested).
In FV = PV(1 + r/(100k))^(kn), what is the per-period multiplier?
1 + r/(100k) — one plus the per-period rate as a decimal.
1.4.28 cards
What is depreciation in terms of a geometric sequence?
Compound decay — a value loses a fixed percentage each year, multiplying by r = 1 − rate (0 < r < 1).
A depreciation question asks 'after how many whole years is it first worth less than $X?'. Method?
Set PV × rⁿ < X with r = 1 − rate, then solve for n (logs or the GDC table) and round UP to the next whole year. It is 'first below', so you need the smallest whole n.
A car worth $24 000 loses 12%/yr. Value after 5 years?
24 000 × 0.88⁵ ≈ $12 666.
A model is V = V₀ × bᵗ. What is the depreciation rate?
1 − b as a percent. E.g. V = 5000(0.92)ᵗ loses 8% a year.
How is depreciation different from compound growth?
Growth multiplies by 1 + rate (> 1); depreciation multiplies by 1 − rate (< 1).
Why doesn't a depreciating value reach zero?
It keeps a fixed percentage each year, so it shrinks geometrically but never actually hits 0.
V = 18 000(0.9)ᵗ — what does the 0.9 mean?
The yearly multiplier: 90% is kept, so 10% is lost each year.
Find the value of a $2000 laptop after 2 years at 30% depreciation.
2000 × 0.7² = 2000 × 0.49 = $980.
1.4.38 cards
What are the TVM solver fields?
N (periods), I% (annual rate as a %), PV (present value), PMT (regular payment), FV (future value), P/Y and C/Y (periods per year).
What is the TVM sign convention?
Money you pay out (invest) is negative; money you receive is positive.
What do you set P/Y and C/Y to?
The compounding frequency: 1 annually, 2 half-yearly, 4 quarterly, 12 monthly. N = years × that frequency.
How do you find an unknown interest rate on the TVM solver?
Enter N, PV (negative), PMT = 0, FV, P/Y = C/Y; leave I% blank and solve.
How do you find how long an investment takes?
Leave N blank, fill I%, PV (negative), PMT = 0, FV, P/Y = C/Y; solve, then round N up (and ÷ frequency for years).
If P/Y = 12, what units is N in?
Months — divide by 12 to get years.
Why round N up in 'how long until' problems?
A part-period hasn't reached the target yet, so you need the next whole period.
When is the TVM solver the quickest method?
On Paper 2 for any compound-interest problem — especially finding the rate or the time, which are awkward by hand.
Topic 1.4 study notes
Full notes & explanations for Financial applications
Math AA SL exam skills
Paper structures, command terms & tips
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