# Application of Differential Equations in Business

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

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

__Example__**:**

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

Here ,

The differential equation governing the given problem is

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

Separating the variables in equation (ii), we have

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

years approximately