An annuity is the same periodic cash flows occurring at the same interval for n periods. There are two types of annuity: ordinary annuity when cash flows occur at the end of each period and annuity due when cash flows happen at the beginning of each period. Here is an example. We are going to receive $100 at the end of each year for the next 7 years. The formulae to estimate the present value and the future value of an annuity are as follows when their first cash flows happens at the end of the first period:

Here, PV is the present value, PMT is the equal periodic payment, R is the periodic discount rate, and n is the number of periods. In the preceding annuity formulae, PMT, R, and n should be consistent. It means that PMT, R, and n should possess the same frequency. For example, for mortgage estimation, PMT is the monthly payment, R is an effective monthly rate, and n is the number of months. If the annuity enjoys a constant growth rate of g, its present value is as follows...