In this chapter, I will introduce some more ideas of basic mathematics including: limits, summation, a geometric series (or the sum of a geometric sequence), the exponential function and logarithms. For some readers these terms may not sound relevant to either economics or finance, but it turns out that they can be powerful in examining various problems in both economics and finance. For example, when we buy a house, a car, or furniture, we may want to borrow money from a bank. Usually borrowing involves a series of repayments and naturally we are interested in the size of the repayments. How will interest be charged on these repayments? Financial institutions often use a procedure that is called daily compounding in calculating interest payments. By using mathematical techniques we learn in this chapter, it turns out the payments can be calculated in a simple manner. Various other ideas in finance will be introduced in this chapter while we go through some mathematics.

Chapter goals By studying this chapter you will

1. (1) become familiar with basic mathematical notions used in financial mathematics, such as limits, summation, geometric series;

2. (2) be able to interpret exponential and logarithmic functions;

3. (3) be able to calculate the net present value of an investment project and make the correct decision on whether to invest; and

4. (4) be able to use a time line to visualise an ordinary annuity and express it using the geometric series.