IB Maths AA SL · Unit 1: Number and Algebra
IB Maths AA SL Financial Math Questions
Exam-style IB Maths AA SL financial math questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
- 26 questions
- Paper 1: 3
- Paper 2: 23
- 8 easy
- 11 medium
- 3 hard
- 2 very hard
- 2 starter
- 3 worked examples
Practise Financial Math questions →
AA SL formula booklet
What's examined in AA SL financial math
The question bank covers these financial math question types (number of questions in brackets):
- Compound Interest Calculations (15)
- Financial Arithmetic Sequences (6)
- Depreciation Modelling (5)
Key formulas
- Compound interest
- \(FV = PV\left(1 + \frac{r}{100k}\right)^{kn}\)
In the same notation as the IB formula booklet. All AA SL formulas →
Financial Math worked examples
Worked example 1: Compound interest calculations · easy
On 1st January, Nerys invests $\text{€}500$ in an account that pays a nominal annual interest rate of $4.2\%$, compounded monthly. Calculate the exact amount of money in the account after $3$ years.
1. Identify the parameters for the compound interest formula: $PV = 500$, $r = 4.2$, $k = 12$ (monthly compounding), and $n = 3$.
2. State the compound interest formula: $FV = PV \times \left(1 + \frac{r}{100k}\right)^{kn}$.
3. Substitute the values into the formula: $FV = 500 \times \left(1 + \frac{4.2}{100 \times 12}\right)^{12 \times 3}$.
4. Simplify the terms in the brackets and exponent: $FV = 500 \times (1.0035)^{36}$.
5. Evaluate the final value using a calculator: $FV = 566.993...$
6. State the final answer rounded to 2 decimal places (standard for currency): $\mathbf{\text{€}566.99}$.
Examiner tip: When using the manual formula instead of the GDC's TVM solver, students often forget to divide the annual interest rate by the compounding periods ($k$), plugging in $4.2/100$ instead of $4.2/1200$.
Worked example 2: Depreciation and finding $n$ · medium
A car is purchased for $\text{€}20000$. Its value depreciates at a rate of $15\%$ per year. Find the number of full years it will take for the car's value to first fall below $\text{€}10000$.
1. Determine the annual multiplier. A $15\%$ decrease means the car retains $85\%$ of its value, so $r = 0.85$.
2. Set up the inequality for depreciation: $20000 \times (0.85)^n < 10000$.
3. Divide both sides by $20000$: $0.85^n < 0.5$.
4. Take the natural logarithm of both sides: $\ln(0.85^n) < \ln(0.5) \implies n \ln(0.85) < \ln(0.5)$.
5. Divide by $\ln(0.85)$. Since $\ln(0.85)$ is negative, you must flip the inequality sign: $n > \frac{\ln(0.5)}{\ln(0.85)} \implies n > 4.265...$
6. Conclude the number of full years required. The next integer is $\mathbf{5 \text{ years}}$.
Examiner tip: Forgetting to flip the inequality symbol when dividing by the logarithm of a number less than $1$ (which is a negative value) is a guaranteed way to lose the final accuracy and reasoning marks.
Worked example 3: Comparing decay models · hard
Machine A's value is modelled by $V_A = 2700 \times (0.82)^t$. Machine B's value is modelled by $V_B = 1100 \times (0.89)^t$, where $t$ is in years. Find the exact time $t$ when both machines have the same value.
1. Set the two value equations equal to each other: $2700(0.82)^t = 1100(0.89)^t$.
2. Group the exponential terms on one side and constants on the other: $\frac{0.89^t}{0.82^t} = \frac{2700}{1100}$.
3. Simplify using exponent laws: $\left(\frac{0.89}{0.82}\right)^t = \frac{27}{11}$.
4. Take the natural logarithm of both sides: $\ln\left(\left(\frac{0.89}{0.82}\right)^t\right) = \ln\left(\frac{27}{11}\right)$.
5. Bring the exponent $t$ down using log laws: $t \ln\left(\frac{89}{82}\right) = \ln\left(\frac{27}{11}\right)$.
6. Solve for $t$: $t = \frac{\ln(27/11)}{\ln(89/82)} = 10.957... \implies \mathbf{11.0 \text{ years}}$ (to 3 s.f.).
Examiner tip: While you can solve this by graphing both functions on your GDC and finding the intersection, AA students should be comfortable setting up and solving these algebraically via logarithms to ensure they can tackle similar Paper 1 questions.
Try these IB Maths AA SL financial math questions
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Question 1 · easy · 8 marks · Paper 2
On his 40th birthday, Robert invests \(\text{€}15\,000\) into a savings account that pays a nominal annual interest rate of \(4.78\%\), compounded monthly.
Write an expression for the total value of the investment after \(n\) years. Give your numerical values to 5 decimal places.
Find the total amount in the savings account after 3 years and 5 years.
Find the exact age Robert will be when the amount of money in his account is \(1.5\) times the initial amount.
Question 2 · medium · 5 marks · Paper 2
Amelia sets a target of saving \(\text{€}20\,000\). She invests her initial \(\text{€}9000\) in an account that offers an interest rate of \(7\%\) per annum compounded annually.
Find the value of Amelia’s investment after 5 years to the nearest hundred euros.
Determine the number of years required for Amelia’s investment to reach the target.
Question 3 · hard · 6 marks · Paper 2
On 1st January 2020, Laurie invests \(\text{€}P\) in an account that pays a nominal annual interest rate of \(5.5\%\), compounded quarterly.
Find the effective annual multiplier (the common ratio \(r\) for the year).
Laurie makes no further deposits to or withdrawals from the account. Using your GDC’s equation solver or financial app, find the exact year and month in which the amount of money in Laurie’s account will become double the amount she invested.
All 26 financial math questions with mark schemes →
FAQ
How many IB Maths AA SL financial math questions are there?
There are 26 exam-style financial math questions in the AA SL question bank (Paper 1: 3 · Paper 2: 23), graded 8 easy, 11 medium, 3 hard, 2 very hard, 2 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is financial math on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 3 · Paper 2: 23. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.
Where can I get the mark schemes?
Open the AA SL Unit 1 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.
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