Financial mathematics.
Learn how investment, savings, retirement and borrowing balances change over time. Use explicit payment timing, rate conventions, deductions and fees, and compare models on consistent assumptions.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Compound-interest revision
Build a compound-interest model using a rate and a number of matching periods, then interpret the balance and interest separately.
- 02
Effective interest rates
Convert quoted nominal rates into effective annual rates so interest models can be compared on the same time scale.
- 03
Savings annuities
Model equal regular deposits, including the difference between depositing at the end and at the beginning of each period.
- 04
Finding deposits, rates, terms and accumulated amounts
Rearrange a savings model to find deposits or time, and use a numerical equation when an unknown rate cannot be isolated conveniently.
- 05
Superannuation models
Use transparent superannuation balance models with stated contribution, tax, fee and return assumptions.
- 06
Annuities providing an income
Find the capital needed for a regular income and track the balance remaining after withdrawals.
- 07
Inflation/tax/fees
Model how taxes, fixed fees and inflation affect balances and purchasing power using only stated assumptions.
- 08
Interest-only loans and sinking funds
Keep the loan and the replacement savings account separate when modelling an interest-only loan with a sinking fund.
- 09
Reducing-balance loans
Track loan interest on the outstanding balance and derive the fixed repayment needed to clear a loan.
- 10
Repayments, outstanding balances and total interest
Find a loan balance partway through its term, calculate a reduced final payment, and separate interest from total repayments.
- 11
Extra repayments, frequency changes and offsets
Model extra repayments, a change in payment frequency, and an offset balance using consistent interest and cash-flow assumptions.
- 12
Comparison rates and choosing between loan models
Compare loan models using consistent principal, term, fees and payment timing rather than choosing by the advertised rate alone.
Topic review
Revisit the key ideas, then choose a practice paper.