Financial applications: compound interest and annual depreciation
Practice Flashcards
What is the IB compound-interest formula?
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All Flashcards in Topic 1.4
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1.4.18 cards
What is the IB compound-interest formula?
FV = PV × (1 + r/(100k))^(kn)
Finance formula
In the IB compound-interest formula, is r entered as 5 or 0.05?
Enter r as 5. The formula already divides by 100.
Percentage, not decimal
What does k mean in compound interest?
k is the number of compounding periods per year. For example: 1 yearly, 4 quarterly, 12 monthly.
Frequency per year
What does kn represent in the formula?
kn is the total number of compounding periods.
Total periods
In the TVM solver, why is PV often negative?
Because the money is leaving your pocket when you invest it. TVM uses cash-flow signs.
Sign convention
What values of k match yearly, quarterly, and monthly compounding?
Yearly: 1. Quarterly: 4. Monthly: 12.
Match frequency
If the TVM solver gives N = 8.3 for a “how many full years” question, what should you state?
9 full years. Round up because 8 full years is not enough.
Full years
What is the difference between simple interest and compound interest?
Simple interest adds the same amount each period, so it is arithmetic. Compound interest multiplies by the same factor each period, so it is geometric.
Arithmetic vs geometric
1.4.28 cards
What multiplier represents 7% growth?
1.07. Keep 100% and add 7%.
Growth means add to 1
What multiplier represents 12% depreciation?
0.88. Keep 88% of the value each period.
Loss means subtract from 1
What is the compound-growth model for r% growth over n years?
A = P(1 + r/100)^n
Repeated percentage growth
What is the depreciation model for r% loss over n years?
A = P(1 - r/100)^n
Repeated percentage loss
Why is 0.10 the wrong multiplier for 10% depreciation?
Because 0.10 is the amount lost, not the amount kept. The correct multiplier is 0.90.
Lost vs kept
A watch costs $400 and depreciates by 5% each year. Write the model.
V = 400(0.95)^n
Depreciation keeps 95%
What should a final finance answer include?
A sensible rounded value and a short sentence in context.
Don’t stop at the number
What does the exponent n count in A = P(1 ± r/100)^n?
The number of percentage-change periods.
Count the periods
1.4.38 cards
What does nominal rate mean?
The advertised annual percentage rate before compounding frequency is taken into account.
Advertised annual rate
What does k mean in FV = PV(1 + r/(100k))^(kn)?
k is the number of compounding periods per year.
Frequency per year
What value of k is used for monthly compounding?
k = 12.
12 months
What does kn represent?
The total number of compounding periods.
Years × periods per year
Which usually gives a larger final value: yearly or monthly compounding at the same nominal rate?
Monthly compounding, because interest is added more often.
More frequent compounding
If the nominal rate is 12% compounded monthly, what is the monthly rate?
1% per month.
12% ÷ 12
Why can two 6% accounts end with different values?
Because different compounding frequencies create different effective yearly growth.
Nominal is not everything
What is the usual final step in a financial comparison question?
Write a decision sentence explaining which option is better and why.
Decide + justify
1.4.48 cards
In a comparison question, what does “better” mean?
It means better for the criterion in the question, such as a larger final balance or lower total cost.
Use the stated criterion
Is a higher interest rate always the better option?
No. The starting amount and compounding frequency can change the final result.
Rate is not everything
What must you compare if two options have different deposits?
The final values that answer the question, not just the deposits or rates separately.
Compare the end result
What is weak about the sentence “Option B is better”?
It gives no mathematical reason.
Need evidence
What is stronger: “B is better” or “B is better because it gives the larger balance after 4 years”?
The second one, because it gives a numerical contextual reason.
Say why
If Option A gives $5624 and Option B gives $5901 after 3 years, which is better?
Option B is better because it gives the larger final balance.
Larger final value wins
What should come after calculating both options?
A comparison and a clear decision sentence.
Don’t stop after calculation
Why do IB finance comparisons often need actual values quoted?
Because unsupported claims like “better” or “more” usually do not earn full marks.
Quote the numbers
1.4.58 cards
What does N mean in TVM?
The total number of periods.
Not just years
If compounding is monthly for 5 years, what is N?
N = 60.
5 × 12
Why is PV often negative in TVM?
Because it is money leaving your pocket at the start.
Cash-flow sign
If the question asks “how long will it take?”, which TVM variable is usually unknown?
N.
Time -> N
What setting should match monthly compounding in TVM?
C/Y = 12, and often P/Y = 12 if there are monthly periods.
Match the frequency
What is a sensible quick check on a compound-growth answer?
The final value should usually be larger than the starting value if the rate is positive.
Sanity-check the direction
Why is N = 6 wrong for 6 years compounded monthly?
Because N must count total periods, so it should be 72.
Years vs periods
When is TVM especially useful?
When the arithmetic is messy or the question asks for an unknown like N, PV, or I%.
Great for messy finance questions
Topic 1.4 study notes
Full notes & explanations for Financial applications: compound interest and annual depreciation
Math AI SL exam skills
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