amount of money you should invest now is: . If you need 25 in 5 years the amount of money you should invest now is: . is the annual effective discount rate: The value of can also be calculated from the following relationships: The rate of discount equals the amount of interest earned during a one-year period, divided by the balance of money at the end of that period. By contrast, an annual effective rate of interest is calculated by dividing the amount of interest earned during a one-year period by the balance of money at the beginning of the year. The present value (today) of a payment of 1 that is to be made years in the future is . This is analogous to the formula for the future (or accumulated) value years in the future of an amount of 1 invested today. , the nominal rate of discount convertible times a year, is analogous to . Discount is converted on an th-ly basis. , the force of interest, is the limiting value of the nominal rate of interest when increases without bound: In this case, interest is convertible continuously. The general relationship between , and is: Their numerical value can be compared as follows: Life tables A life table (or a mortality table) is a mathematical construction that shows the number of people alive (based on the assumptions used to build the table) at a given age. In addition to the number of lives remaining at each age, a mortality table typically provides various probabilities associated with the development of these values. is the number of people alive, relative to an original cohort, at age . As age increases the number of people alive decreases. is the starting point for : the number of people alive at age 0. This is known as the radix of the table. Some mortality tables begin at an age greater than 0, in which case the radix is the number of people assumed to be alive at the youngest age in the table. is the limiting age of the mortality tables. is zero for all . is the number of people who die between age and age . may be calculated using the formula is the probability of death between the ages of and age . is the probability that a life age will survive to age . Since the only possible