Business Mathematics presents math skills and knowledge that you
can apply to solve financial problems. Finance plays a major role
in our lives--car loans, mortgage payments, retirement plans, real
estate investment--and knowing how to calculate the cost of
borrowing or the return on investment is important to us. The
course provides step-by-step guidance through sample problems and
solutions related to banking, credit, basic finance and investment.
You will also gain an understanding of financial instruments and
terminology used in business finance such as compound interest,
annuities and promissory notes.
Portfolio theory introduces the theory and practice of modern
portfolio theory and its application to investment analysis. The
subject introduces the foundations of investment decision making
under uncertainty, utility theory and portfolio selection via the
mean-variance approach. The capital asset pricing model and the
single index model are also developed.
Time value of money. Compounding and
discounting single sums: future value and present value, interest
and discount factor. Simple interest. Compound interest and
compound discount. Equivalent rates. Nominal and effective annual
interest rates. Continuous compounding and discounting.
Annuities and loan repayment. Ordinary annuity
and annuity due. The present value and the future value of an
annuity. Perpetuities. Discounting of continuous cash flows.
Amortization with constant instalments and with constant principal
payments. Outstanding principal. Amortization plan. Adjustable-rate
Financial project evaluation (under certainty).
Methods for investment evaluation and choice. Discounted Cash Flow
(DCF) and Internal Rate of Return (IRR): definition, properties and
financial meaning. Annual Percentage Rate.
Bond valuation and yield curve. Term structure
of interest rates. Spot rates and forward rates. Yield to maturity.
Valuation of risky investments. Choice under
uncertainty, expected value, expected utility, stochastic
dominance. Mean-variance criterion. Risk and volatility. Value at
Portfolio Theory. Portfolio Selection: Markowitz Model.
Single-index models. Capital Asset Pricing Model (CAPM)
D. Lovelock, M. Mendel, A.L. Wright, An Introduction to the
Mathematics of Money: Saving and Investing. Springer, 2007;
S.A. Broverman, Mathematics of Investment and Credit (3rd
edition ), Actex Publications, 2004.
Edwin J. Elton, Martin J. Gruber, Stephen J. Brown, William N.
Goetzmann, Modern portfolio theory and investment analysis. John
D.G. Luenberger, Investment Science, Oxford University Press,
The exercises and problems presented and discussed in the
classroom are essential to properly understand all the parts of the
program. In the written exam, the student will be required to solve
specific exercises using the tools and techniques learnt in the
The examination consists of a written part and an oral part
The written exam is open book and students are welcome to bring
their own reference material (books, notes, scientific calculator),
for strictly personal use. No one will be allowed to exit the
classroom after the written exam has begun.
Only students who pass the written part will be admitted to the
oral exam, to be taken only in the scheduled dates. Students who do
not take the oral examination in the scheduled date will be deemed
to have withdrawn from the exam
The oral exam consists of two phases
A a discussion of the written exam, during which the
student will be required to justify his/her answers to the
B an interview about the main theoretical results, their
applications, and topics which require a more in-depth knowledge of
Students are allowed to stop the oral exam just after phase
A, if they estimate that their overall performance should
not be worth more than 18/30
- PC connected projector
Language of instruction