One of the themes we will see many times in the study of financial mathematics is the comparison of the value of a particular investment at the present time with the value of the investment at some point in the future. This is the comparison between the present value of an investment versus its future value. We will see in this section that present and future value play central roles in planning for retirement and determining loan payments. Later in this book present and future values will help us determine a fair price for stock market derivatives