# The Application of Differential Equations in Business

In the following example we shall discuss the application of simple differential equation in business.

If is the principal amount and is the rate of interest, then the differential equation relating to the time , and is

__Example__**:**

How long will it take for Rs.10000 to double if it is compounded continuously at 4 percent per annum?

Here ,

The differential equation governing the given problem is

Since the rate is fixed, putting the values of in equation (i), we have

Separating the variables in equation (ii), we have

Since the time during which is doubled is to be calculated, integrating the left hand side of equation (iii) from 10000 to 20000 and integrating its right hand side from 0 to , we have

years, approximately.