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
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Time value of money
Simple vs compound interest
Coming soon - Fixed income and projects
Bond price–yield relationships
Coming soon - Uncertainty and markets
Mean–variance portfolio math (intro)
Coming soon
Notes
May be housed in economics, finance, or math departments. Depth of stochastic calculus is out of scope unless the course requires it.