IB Maths AI SL · Unit 1: Number and Algebra
IB Maths AI SL Financial Mathematics Questions
Exam-style IB Maths AI SL financial mathematics questions with worked solutions. Start with the 4 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.
- 47 questions
- Paper 1: 15
- Paper 2: 32
- 5 easy
- 13 medium
- 15 hard
- 8 very hard
- 6 starter
- 4 worked examples
Practise Financial Mathematics questions →
AI SL formula booklet
What's examined in AI SL financial mathematics
The question bank covers these financial mathematics question types (number of questions in brackets):
- Lump Sum Growth/Decay (25)
- Loan Repayment/Payouts (16)
- Regular Savings Annuities (6)
Key formulas
- Compound interest
- \(FV = PV\left(1 + \frac{r}{100k}\right)^{kn}\)
In the same notation as the IB formula booklet. All AI SL formulas →
Financial Mathematics worked examples
Worked example 1: Compound interest with quarterly compounding · easy
Leo invests $\text{€}6000$ in a savings account that pays a nominal annual interest rate of $3.2\%$, compounded quarterly. Calculate the total value of Leo's investment after $5$ years.
1. Identify GDC parameters: $N = 5 \times 4 = 20$, $I\% = 3.2$, $PV = -6000$.
2. Set compounding frequencies: $P/Y = 4$, $C/Y = 4$.
3. Solve for $FV$ on the GDC financial solver.
4. Read the output: $FV = 7036.711\ldots$
5. State: total value $= \mathbf{\text{€}7036.71}$.
Examiner tip: Enter $PV$ as a negative number to represent cash flowing FROM you INTO the bank. Money answers should be rounded to 2 d.p.
Worked example 2: Depreciation time to halve · medium
A car is purchased for $\text{€}28\,000$ and depreciates at a rate of $12\%$ per year. Using your GDC, find the exact number of years it will take for the car's value to halve.
1. Target value: half of $\text{€}28\,000 = \text{€}14\,000$.
2. Set up: $V = PV(1 - r)^t \implies 14000 = 28000(1 - 0.12)^t$.
3. Simplify: $0.5 = 0.88^t$.
4. Solve using the GDC (equation solver or graph intersection of $Y_1 = 0.88^x$ and $Y_2 = 0.5$).
5. Read the intersection: $t = 5.4222\ldots \implies \mathbf{5.42\text{ years}}$.
Examiner tip: Depreciation = compound interest with a negative rate. On the GDC you can also enter $I\% = -12$ and solve for $N$.
Worked example 3: Loan amortisation and total interest · hard
A family takes out a mortgage of $\text{€}350\,000$ over $25$ years at a nominal annual interest rate of $4.8\%$, compounded monthly. Calculate the monthly repayment, and hence the total interest paid over the life of the loan.
1. Identify GDC parameters: $N = 300$, $I\% = 4.8$, $PV = 350000$, $FV = 0$, $P/Y = 12$, $C/Y = 12$.
2. Solve for $PMT$: the GDC gives $PMT = -2005.474\ldots \implies$ monthly repayment $= \mathbf{\text{€}2005.47}$.
3. Total paid to the bank over $25$ years: $2005.47 \times 300 = \text{€}601\,641.00$.
4. Subtract the principal: $601641 - 350000$.
5. State: total interest paid $= \mathbf{\text{€}251\,641.00}$.
Examiner tip: When calculating total interest paid, use the ROUNDED monthly repayment (to 2 d.p.) multiplied by the total number of months — that reflects what actually leaves the bank account.
Worked example 4: Future value of an annuity · hard
Sarah deposits $\text{€}300$ at the end of every month into a savings account paying a nominal annual interest rate of $4.2\%$, compounded monthly. Calculate the total value of her account after $10$ years.
1. Recognise this is an annuity (regular payments) — use the GDC financial solver.
2. Set $N = 120$, $I\% = 4.2$.
3. Set cash flows: $PV = 0$, $PMT = -300$ (cash out of pocket).
4. Set $P/Y = 12$, $C/Y = 12$.
5. Solve for $FV$.
6. Read: $FV = 44648.51\ldots \implies \mathbf{\text{€}44\,648.51}$.
Examiner tip: For an annuity, $PMT$ is negative (out of pocket) and $PV$ is $0$ unless there was an initial balance. Do not conflate an annuity with a lump-sum investment.
Try these IB Maths AI SL financial mathematics 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 · 4 marks · Paper 1
David invests \(\text{€}6000\) in a bank account that pays \(3.5\%\) p.a. simple interest for 4 years.
Calculate the total interest earned over the 4 years.
Calculate the total value of the investment at the end of the 4 years.
Question 2 · medium · 6 marks · Paper 1
Isabella invests \(\text{€}15\,000\) in an account paying \(6.5\%\) nominal annual interest, compounded annually for 8 years. The average rate of inflation over this period is expected to be \(2.4\%\) per year.
Calculate the nominal value of the investment after 8 years.
Calculate the approximate real interest rate.
Calculate the real value of the investment after 8 years, taking inflation into account.
Question 3 · hard · 9 marks · Paper 2
A family takes out a mortgage of \(\text{€}200\,000\) to buy a house. The loan is amortized over 20 years at a nominal annual interest rate of \(4.5\%\), compounded monthly. Fixed repayments are made at the end of each month. The monthly repayment is \(\text{€}1265.30\), correct to the nearest cent.
Using your GDC, calculate the outstanding balance (the amount still owed) at the end of exactly 5 years.
Calculate the amount of the principal that has been paid off during the first 5 years.
Calculate the total interest paid during the first 5 years.
All 47 financial mathematics questions with mark schemes →
FAQ
How many IB Maths AI SL financial mathematics questions are there?
There are 47 exam-style financial mathematics questions in the AI SL question bank (Paper 1: 15 · Paper 2: 32), graded 5 easy, 13 medium, 15 hard, 8 very hard, 6 starter. Every question has a full IB-style mark scheme (M, A and R marks).
Is financial mathematics on Paper 1 or Paper 2?
Both. In the bank, Paper 1: 15 · Paper 2: 32. Practise with your GDC — AI papers expect calculator methods throughout.
Where can I get the mark schemes?
Open the AI 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.
← All IB Maths AI SL topics