1. Introduction

In the preceding section, we have learned how to compute the future value of investments with annual interest payments. More precisely, we have used a formula that is designed for investments that make exactly one interest payment per investment period. In our example, an investment period was 1 year and the investment paid its return once per year at the end of the year. Therefore, we have treated time consistently in the definition of the interest rate (R) and the number of investment periods (T-t):

  

\( FV_T = C_t \times (1+R)^{(T-t)} \)

  

However, it need not necessarily be the case that investments make annual interest payments. Very often, interest payments are semi-annually or even quarterly. For example, typical mortgage terms could be that the mortgage carries an annual interest rate of 4%, payable in quarterly rates of 1% at the end of each quarter.

How can we compute the future value of such assets? That is the topic of this section.