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.

Nominal $FV = 15000(1.065)^8$ (M1) $= \text{€}24\,824.94$ ( $24824.935\dots$ ) A1 Real rate $\approx$ nominal rate $-$ inflation rate $= 6.5\% - 2.4\% = 4.1\%$ (M1)A1 Use the real rate: Real $FV = 15000(1.041)^8$ (M1) $= \text{€}20\,686.98$ ( $20686.980\dots$ ) A1

IB Maths AI SL · Unit 1: Number and Algebra

Financial Maths (IB Maths AI SL): notes, exam questions and worked examples

Updated October 2026 · By Pete Bromfield

Financial maths in AI SL is compound growth: savings and loans grow by the same percentage each period, assets lose value by depreciation, and regular payments (annuities and loan repayments) are handled with the TVM solver on your GDC. Set the number of periods, the interest rate, present value, payment and future value, and keep the signs right: money you pay out is negative.

47 questions
Paper 1: 15
Paper 2: 32
3 worked examples

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Notes
Formulas
Worked examples
Questions
FAQ

Financial Maths notes

Compound interest

$F V = P V {(1 + \frac{r}{100 k})}^{k n}$ , where $r$ % is the annual rate, $k$ the number of compounding periods a year and $n$ the number of years. For example \$1000 at 4% compounded quarterly for 5 years grows to $1000 (1.01)^{20} \approx $ 1220.19$ . The formula is in the booklet; the work is reading $k$ correctly ("monthly" means $k = 12$ ).

Depreciation

An asset losing $r$ % of its value each year is worth $V = V_{0} {(1 - \frac{r}{100})}^{n}$ after $n$ years. A \$20\,000 car losing 15% a year is worth $20 000 (0.85)^{3} \approx $ 12 282.50$ after 3 years. This formula is not in the booklet, so learn it.

The TVM solver

For anything with regular payments, use the finance (TVM) app: N (number of payments), I% (annual rate), PV, PMT, FV, P/Y (payments a year) and C/Y (compounding periods a year). Enter the four you know and solve for the fifth. Money you hand over (a deposit, a repayment) is negative and money you receive is positive, so a loan has a positive PV and a negative PMT. Write down every value you entered: that is your working.

Loans and amortisation

A loan is paid off when FV = 0. The total paid is the payment times the number of payments, and the total interest is the total paid minus the amount borrowed. An amortisation table shows each payment split into interest and the part that reduces the balance.

Annuities and savings plans

An annuity pays (or saves) a fixed amount each period. For a savings plan, PV is the starting amount and FV the target; for an annuity paid out from a fund, PV is the fund and FV is usually 0. Read whether payments are made at the start or end of each period if the question says.

Key formulas

Compound interest ( $k$ times a year, $n$ years, $r$ %) In the booklet: $F V = P V {(1 + \frac{r}{100 k})}^{k n}$
Depreciation at $r$ % a year Learn it: $V = V_{0} {(1 - \frac{r}{100})}^{n}$

The IB formula booklet is provided in every exam paper. In the booklet = printed there, so know where to find it; Learn it = not in the booklet, so learn it by heart. All AI SL formulas →

Explained, with a worked example: Compound interest

Financial Maths worked examples

Worked example 1: Compound interest with quarterly compounding · easy

Leo invests $€ 6000$ 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.

Solution

5 steps

Examiner tip: Enter

P V

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 $€ 28 000$ 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.

Solution

5 steps

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 $€ 350 000$ 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.

Solution

5 steps

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.

Financial Maths exam-style questions

3 questions from our AI SL bank, written in the style of IB papers, easiest first. One has its full worked solution open here. Open the worked answer, or check your answer in the practice area.

Question 1 · easy · 4 marks · Paper 1

David invests $€ 6000$ 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.

Check your answer in practice →

Question 2 · medium · 6 marks · Paper 1

Isabella invests $€ 15 000$ 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.

Full worked solution Free, no sign-in

Nominal $F V = 15000 (1.065)^{8}$ (M1)
$= € 24 824.94$ ( $24824.935 \dots$ ) A1
Real rate $\approx$ nominal rate $-$ inflation rate $= 6.5 % - 2.4 % = 4.1 %$ (M1)A1
Use the real rate: Real $F V = 15000 (1.041)^{8}$ (M1)
$= € 20 686.98$ ( $20686.980 \dots$ ) A1

Every question here has a full worked solution. See them all →

Question 3 · hard · 9 marks · Paper 2

A family takes out a mortgage of $€ 200 000$ 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 $€ 1265.30$ , 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.

Attempt it and see the mark scheme →

Free account — sign in to download Topic PDF: 7 questions with worked answers · 5 pages · 255 KB

All 47 financial maths questions →

Where students lose marks on financial maths

Examiner's noteFinance: compound-interest formula with regular payments, TVM signs and periods

Where marks are lost: Every session: the compound interest formula was used where regular payments made it invalid; PV and PMT had the same sign; N was entered in years instead of months; P/Y and C/Y were confused; answers were not given to the nearest dollar or 2 decimal places as asked; and the interest paid was confused with the interest rate.

What examiners look for: With regular payments, use the TVM solver. Money in and money out have opposite signs. N counts payments (years × payments per year). Write down every value you enter (N, I%, PV, PMT, FV, P/Y, C/Y), so a slip can still earn method marks.

Examiners flagged this in 3 exam series (May 2024, November 2024, November 2025). Summarised in our own words from IB subject reports, IB Programme Resource Centre. Read the full note →

Financial Maths on your calculator

A GDC is allowed on every AI paper. Keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire, with a checked worked example:

Finance (TVM solver) on your calculator

Financial Maths FAQ

Is the compound interest formula in the IB formula booklet?

Yes, the AI SL booklet gives FV = PV(1 + r/100k)^(kn). The depreciation formula is not printed, and loans and annuities are done on the GDC's TVM solver, so practise entering N, I%, PV, PMT, FV, P/Y and C/Y.

Why does the TVM solver give a negative answer?

The solver uses signs for the direction of money: what you pay out is negative and what you receive is positive. A negative PMT on a loan just means you are paying it. Quote the size of the amount in your answer.

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 6 easy, 18 medium, 15 hard, 8 very hard. 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.

Next steps

More AI SL Unit 1: Approximations and Error · Logarithms and Exponentials · Systems of Equations · Volume and Surface Area

Teaching this topic? Free ready-to-teach lessons (slides and teacher notes): Simple & compound interest · Amortisation & annuities on the GDC.

Keep revising AI SL: AI SL revision notes · IB Maths AI SL past papers · AI SL common exam mistakes · AI SL syllabus checklist · AI SL number and algebra knowledge organiser

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← All IB Maths AI SL topics

Financial Maths (IB Maths AI SL): notes, exam questions and worked examples

Try it first

Financial Maths notes

Compound interest

Depreciation

The TVM solver

Loans and amortisation

Annuities and savings plans

Key formulas

Financial Maths worked examples

Worked example 1: Compound interest with quarterly compounding · easy

Solution

Worked example 2: Depreciation time to halve · medium

Solution

Worked example 3: Loan amortisation and total interest · hard

Solution

Financial Maths exam-style questions

Question 1 · easy · 4 marks · Paper 1

Question 2 · medium · 6 marks · Paper 1

Full worked solution Free, no sign-in

Question 3 · hard · 9 marks · Paper 2

Where students lose marks on financial maths

Financial Maths on your calculator

Financial Maths FAQ

Next steps

What else is free here