Mathematics of finance
Undergraduate · Economics
Syllabus focus
Topics typically covered
Standard syllabus
Time value of money
- Simple vs compound interest
- Effective rates and continuous compounding
- Present and future value of lump sums
- Annuities and perpetuities
- Amortization schedules
- Nominal vs real rates and inflation adjustments
Fixed income and projects
- Bond price–yield relationships
- Duration and interest-rate sensitivity (intro)
- Spot rates and forward rates (intro)
- Capital budgeting: NPV and IRR
- Comparing mutually exclusive projects
- Credit risk awareness (survey)
Uncertainty and markets
- Mean–variance portfolio math (intro)
- Diversification and correlation
- CAPM intuition and beta (survey)
- Options payoff diagrams (intro)
- Put–call parity awareness
- Arbitrage intuition in simple one-period models
STEM / applied
Computational practice
- Spreadsheet PV/FV/NPER/RATE formulas
- Building amortization tables
- Bond pricing calculators
- Simulating portfolio returns
- Solving IRR numerically
- Checking formulas against financial calculator results
Applications
- Mortgage and student-loan comparisons
- Corporate project evaluation cases
- Interpreting yield quotes from markets
- Risk communication for non-quants
- Ethics of disclosure in financial products
- Capstone: analyze a financing decision with full TVM work
Notes
May be housed in economics, finance, or math departments. Depth of stochastic calculus is out of scope unless the course requires it.