Suppose we decide to invest some money in an account that continously compounds interest. In other words, the amount that we initially invested is constantly earning interest and any interest that we earned also keeps acquiring interest. At first, let's compute our earnings in the short term. Suppose you save $100 each month into a savings account that has an annual interest rate of 5%. So, the monthly interest rate is 0.05/12 : 0.00417. After the first month, the value in the account becomes 100 a: (1 + 0.00417) : 100.417 After the second month, the value in the account becomes (100 4 100.417) :1: (1 4 0.00417) 2 201.252 After the third month, the value in the account becomes (100 201.252) * (1 0.00417) : 302.507 :Inrl en n