STAT2032 Financial Mathematics
The Complete Exam Bible · S2 2026STAT2032 Overview
- Australian National University
- Semester 2, 2026
- Undergraduate
- On campus final
- Closed book final
What the course is about
Financial Mathematics studies how money at different dates becomes comparable. The course begins with cash-flow models and the language of interest: simple and compound accumulation, effective and nominal rates, discount, force of interest and rate conversion.
- Final format Three hours, on campus and invigilated, with theoretical and numerical questions across the entire semester.
- Permitted aid A non-programmable calculator is allowed. The published final conditions say closed book and no dictionaries.
- Central method Put every cash flow on one timeline, convert the rate to the matching period and choose one focal date.
What you get in the full STAT2032 Exam Bible
- 8 chapters, 45 pages — every examinable topic, week by week
- 28 original practice questions, most with model answers in the Final Exam format
- 8 worked examples, solved the way STAT2032 marks
- 11 computed figures, redrawn from the course’s own numbers
- Exam-morning plan for the Final Exam (75%) — what to revise last, where marks are lost
Free on this page: assessment table, chapter map, one worked example, key terms, FAQ. The rest is in the full exam bible.
How STAT2032 is assessed
| Component | Weight | Format |
|---|---|---|
| In-class tests (2, weeks 5 and 10; best 1 of 2 counts) | 5% | Held 24 August and 12 October 2026. Each is closed book and lasts ten to twenty minutes, with written, multiple-choice and calculation questions. Test 1 covers weeks 1 to 4 and Test 2 covers weeks 5 to 8; the best result counts. |
| Assignment | 20% | Due 16 October 2026. Material through the ninth teaching week, using spreadsheet, document and presentation software, with a prerecorded video shorter than ten minutes. |
| Final Exam | 75% | Due 5 November 2026. Three-hour on-campus invigilated closed book examination across the entire semester, with theoretical and numerical questions and a non-programmable calculator allowed. |
Students sit two in-class tests in weeks 5 and 10, and Assessment Task 1 states that the best one of the two results counts for 5% overall. The assignment is 20% and the final examination is 75%. No hurdle or component minimum is stated.
Published assessment weights
What other students are asking about STAT2032
- Where can I find lecture notes or study guides for STAT2032 at anu?
- The STAT2032 study guide in AskSia Library covers Financial Mathematics in 8 chapters, with the assessment table, a chapter-by-chapter topic map, key terms and a worked example, free to read on this page.
- Is there a final exam in STAT2032, and how much is it worth?
- Yes. In the offering this AskSia Library guide is built from, Final Exam carries 75% of the STAT2032 mark; the full split is In-class tests (2, weeks 5 and 10; best 1 of 2 counts) 5%, Assignment 20%, Final Exam 75%.
- What does STAT2032 cover on annuity valuation?
- In AskSia Library's STAT2032 guide, the Annuity Valuation chapter explains level, deferred and varying payment streams.
- What does STAT2032 cover on equations of value and inflation?
- In AskSia Library's STAT2032 guide, the Equations of Value and Inflation chapter explains focal dates, roots and purchasing power.
- What does STAT2032 cover on loans and capital budgeting?
- In AskSia Library's STAT2032 guide, the Loans and Capital Budgeting chapter explains balances, project value and return.
Current STAT2032 dates
| Date | Item | Control |
|---|---|---|
| 24 August 2026 | In-Class Test 1 | Published in the official assessment summary. |
| 12 October 2026 | In-Class Test 2 | Published in the official assessment summary. |
| 16 October 2026 | Assignment | Published in the official assessment summary. |
| 5 November 2026 | Final Exam | Published in the official assessment summary. |
Dates are as published in the official Semester 2, 2026 class summary. Confirm exact deadlines and submission settings in the live LMS.
What STAT2032 covers
Eight chapters follow the published sequence from cash flows and rates through annuities, equations of value, loans, capital budgeting and performance measurement to securities, the term structure and immunisation.
Cash Flows and Interest Rates
Timing, accumulation and rate conversionEvery later valuation in the course depends on two decisions made here: where each cash flow sits in time and what period the interest quotation describes.
- Cash-flow signs and valuation dates
- Simple and compound accumulation
- Present value and discount factors
- Effective and nominal rate conversion
- Discount rates and force of interest
- Fractional valuation periods
Annuity Valuation
Level, deferred and varying payment streamsAn annuity formula is a compressed cash-flow schedule, so timing comes before notation.
- Annuity immediate timing
- Annuity due timing
- Deferred level payments
- Perpetuity boundaries
- Increasing and decreasing streams
- Continuous and indexed annuities
Equations of Value and Inflation
Focal dates, roots and purchasing powerAn equation of value makes unlike cash-flow dates comparable by moving every amount to one chosen focal date.
- Choosing a focal date
- Accumulating earlier cash flows
- Discounting later cash flows
- Unknown yield equations
- Bracketing and interpolation
- Nominal and real returns
Loans and Capital Budgeting
Balances, project value and returnLoans and projects are both equations of value, but their questions point in different directions.
- Level loan repayments
- Interest and principal splits
- Prospective loan balances
- Retrospective loan balances
- Net present value
- Internal rate of return
Investment Performance
Money weighted and time weighted returnsA fund history can support different return measures because external cash flows change whose experience is being measured.
- External and internal cash flows
- Money-weighted return equations
- Time-weighted segment returns
- Linking growth factors
- Investor and manager perspectives
- Income and cash-flow classification
Fixed Interest Securities
Coupon cash flows, yield and redemptionA fixed interest security is valued from promised cash flows, not from its label. A coupon bond combines a level coupon stream with a redemption payment, each discounted at a yield expressed for the coupon period.
- Coupon and redemption cash flows
- Yield per coupon period
- Premium and discount bonds
- Valuation between coupon dates
- Optional redemption dates
- Inflation and tax adjustments
Term Structure of Interest Rates
Spot rates, forward rates and curve shapesThe term structure replaces the shortcut of one yield for all maturities. A spot rate discounts one cash flow from today to its particular maturity, while a forward rate describes a future interval implied by current spot rates.
- Spot rates by maturity
- Discount factors from spots
- Forward rates for future intervals
- No-arbitrage accumulation paths
- Bond pricing on a spot curve
- Normal, flat, inverted and humped curves
Duration, Convexity and Immunisation
Price sensitivity and liability protectionDuration and convexity translate a list of discounted cash flows into local interest-rate sensitivity.
- Present-value cash-flow weights
- Macaulay duration
- Modified duration
- Price-yield convexity
- First and second-order approximations
- Present value and duration matching
The central discipline is to identify the timing unit before applying a factor.
Once that habit is secure, an annuity is simply a structured collection of cash flows, a loan is an equation of value with a changing balance, and a fixed interest security is a coupon annuity plus a redemption payment.
How the topics build
The published schedule places cash flows and rates in the first two teaching weeks, annuities in the next two, equations of value and inflation in the fifth, and loans and capital budgeting in the sixth.
Investment performance follows, with money-weighted and time-weighted returns answering different questions about the same fund history. Fixed interest securities occupy the next block, then the course moves from a single yield to the term structure of spot and forward rates.
Duration, convexity and immunisation finish the sequence by turning bond valuation into a local analysis of interest-rate risk.
What makes the final demanding
The official description calls the final a three-hour, closed-book, on-campus and invigilated examination containing theoretical and numerical questions over the entire semester. A non-programmable calculator is allowed and dictionaries are not.
That combination rewards more than formula recall. A numerical solution needs a defensible cash-flow line, a rate in the correct period, a clear equation of value and a reasonableness check.
A theoretical solution needs the mechanism connecting quantities, such as why present value falls when the discount rate rises or why time-weighted return removes the impact of external cash-flow timing.
How to work with this guide
Each chapter starts from the relationship that governs the topic and then uses original numbers to expose common errors.
The diagrams are functional: they show timing, direction, segmentation, term or sensitivity rather than decorating a definition. Recalculate every worked result, then vary one input and predict the direction before using a calculator. The final practice bank mixes short theory explanations with calculations because that is the only question-type split the official source publishes.
It does not imitate a paper structure or mark scheme that the source does not provide.
Worked example · free
Price a coupon bond from its cash flows
- 1Convert the effective annual yield to the half-year period: j = (1.07)^(1/2) - 1 = 0.034408.
- 1Identify ten coupons of $30 and a $1,000 redemption with the last coupon.
- 1Value the cash flows: P = 30a at j for ten periods + 1000v^10.
- 1The calculation gives P = $963.23, subject to rounding from the retained periodic yield.
- 1Because the required half-year yield exceeds the 3% coupon rate, the price is below par, which confirms the direction.
Key terms
- Accumulation function
- The factor that moves one unit of value forward from one date to another under a stated interest model.
- Effective interest
- Interest earned during a period divided by the amount held at the start of that period.
- Nominal rate
- An annual quotation whose stated conversion frequency determines the periodic rate used in valuation.
- Force of interest
- The continuously compounded rate, linked to effective interest by the logarithm of the annual accumulation factor.
- Annuity immediate
- A level payment stream whose first payment occurs at the end of the first valuation period.
- Annuity due
- A level payment stream whose first payment occurs immediately, one period earlier than an annuity immediate.
- Equation of value
- An equality formed after moving every relevant cash flow to the same focal date at a common valuation basis.
- Prospective balance
- The present value at the balance date of the loan repayments that remain after that date.
- Net present value
- The value at the chosen discount rate of project inflows less the value of project outflows.
- Time weighted return
- A linked return across clean subperiods that removes the effect of external cash-flow size and timing.
- Spot rate
- The yield applying from the valuation date to one specific maturity for a single future cash flow.
- Forward rate
- The rate for a future interval implied by spot rates when alternative accumulation paths have equal value.
- Macaulay duration
- The present-value-weighted average payment time of a fixed cash-flow security.
- Convexity
- A second-order measure of curvature in the relationship between a security price and its yield.
STAT2032 FAQ
What is published about the final examination?
The official class summary describes a three-hour, on-campus and invigilated final that is closed book. It covers the entire semester and contains theoretical and numerical questions. A non-programmable calculator is allowed and dictionaries are not. It does not publish a section count or per-question mark scheme.
How do the two in-class tests contribute to the course grade?
Students sit two in-class tests during tutorial times in weeks 5 and 10. Assessment Task 1 states that the best one of the two results counts, contributing five per cent overall. The assignment contributes twenty per cent and the final examination contributes seventy-five per cent.
What is the safest first step in a valuation problem?
Draw the cash-flow line before selecting a formula. Mark time zero, payment dates, signs and the period unit. Then convert the quoted rate to that same period and choose the focal date. This order prevents a correct formula from being applied to the wrong timing convention.
How can I distinguish an annuity immediate from an annuity due?
Look at the first payment date, not the wording around the stream. An immediate annuity first pays at the end of the first period. A due annuity first pays at the beginning, so every payment is one period earlier and the value is one accumulation factor larger at the same focal date.
When should a loan balance be calculated prospectively?
The prospective method is natural when the remaining payment schedule is easy to identify: value only the repayments after the balance date. It also makes the timing instant important. A balance immediately after a payment excludes that payment, while a balance immediately before it still includes the amount then due.
Why can money weighted and time weighted returns differ?
Money-weighted return solves an equation using the actual dates and sizes of external contributions and withdrawals, so it reflects the investor's timing. Time-weighted return splits the history at those flows and links the clean growth factors, so it isolates the underlying investment performance from new money.
How do I predict whether a bond is above or below par?
For a bond redeemable at par, compare the coupon rate per payment period with the required yield per the same period. If the yield is higher, the promised coupons are less attractive and price is below par. If the coupon rate is higher, price is above par.
Why are duration and convexity both used in immunisation?
Matching present value aligns the asset and liability levels, and matching duration aligns their local slopes with respect to yield. Convexity then compares curvature. Requiring asset convexity to be at least liability convexity gives the surplus protective local bending around the matching yield rather than only a tangent match.
Questions students ask in each STAT2032 chapter
- Why can I not use a nominal annual rate directly?
- A nominal quotation packages a periodic rate and a conversion frequency. Its number is divided by that frequency to obtain the rate applied each conversion period. If cash flows occur monthly, use the monthly rate and a monthly time count, or first convert the quotation into an equivalent effective rate for the period you need. Chapter 01 · Cash Flows and Interest Rates
- Where is the natural valuation date for an annuity immediate?
- For a level annuity immediate, the standard present value is dated immediately ahead of its first cash flow. If the first payment is at time one, that date is time zero. If the stream begins later, first place the annuity value at that preceding date and then discount that single value to the required focal date. Chapter 02 · Annuity Valuation
- Does the focal date change the answer?
- Under one consistent interest model, equivalent equations written at different focal dates contain the same information and produce the same unknown rate or payment. The numerical terms look different, but multiplying the whole equation by a common accumulation factor moves one version into the other. Inconsistent rate periods or missing cash flows break that equivalence. Chapter 03 · Equations of Value and Inflation
- Why do loan payments contain changing principal amounts?
- Interest for a period is charged on the opening balance. With a level repayment, the remainder reduces principal. As the balance falls, the next interest charge falls, leaving more of the unchanged payment for principal. This is why the interest portion declines and the principal portion rises across an ordinary amortisation schedule. Chapter 04 · Loans and Capital Budgeting
- Which return measures manager performance?
- Time-weighted return is designed to remove the effect of external contributions and withdrawals that the manager does not control. It splits the measurement period at those flows and links the clean growth factors. Money-weighted return can still be the right measure for the investor, because it reflects how much money was exposed during each part of the path. Chapter 05 · Investment Performance
- Why does a higher yield produce a lower bond price?
- The promised coupons and redemption do not change when the required yield changes. A higher yield applies stronger discounting to each positive future cash flow, so their present values fall and the price falls. The relationship is inverse and curved because cash flows at different dates receive different powers of the discount factor. Chapter 06 · Fixed Interest Securities
- Why does each cash flow use a different spot rate?
- A spot curve assigns a market discount rate to each maturity. A coupon at year one and a redemption at year five belong to different maturities, so they use different discount factors. Summing their separately discounted values prices the security without imposing the extra assumption that one flat yield applies at every date. Chapter 07 · Term Structure of Interest Rates
- Why is Macaulay duration measured in time?
- Its weights are each cash flow's present value divided by total price, and those weights sum to one. Multiplying each weight by its payment time and adding produces a weighted average time. Modified duration then rescales that time measure by yield to express local percentage price sensitivity. Chapter 08 · Duration, Convexity and Immunisation
How to study for the exam
Work in the published topic order because each later method reuses earlier valuation mechanics. Start by converting rates without looking at notes, then draw cash-flow lines for immediate, due and deferred annuities. For loans, calculate the same balance prospectively and retrospectively until both timing conventions agree.
For capital budgeting, separate the required discount rate used for NPV from the unknown rate solved as IRR. In the performance chapter, classify every movement as investment growth or an external contribution or withdrawal before choosing MWRR or TWRR. Price one coupon bond by discounting individual flows, then compress the same calculation into annuity notation.
Rebuild forward rates from equal accumulation paths instead of memorising isolated formulas. Finish by computing present-value weights, duration and convexity from one cash-flow set, and state the three immunisation conditions in words. Under closed-book conditions, practise writing the equation first and calculator entries second.
After every answer, record the rate period, the focal date, the units and one directional reasonableness check. The official source provides no final-paper sample, so vary the context and numbers rather than memorising a guessed section format.
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