Q. 295.0( 1 Vote )

In a bank, the principal increases continuously at the rate of r% per year. Find the value of r if Rs. 100 double itself in 10 years (Take loge2 = 0.6931).

Answer :

Let the Principle be p

Since, it is given principle is increasing continuously at a rate of r% per year


Therefore,





Integrating both sides



Since,






Taking anti - log both side


…(i)


Since, Time = 0 , then principal = 100


If , Time = 10 , then principal = 200 (Double ) Given


So, putting t = 0 and p = 100 in equation (i)





C = 100


Now, Put the value of C in equation (i), we get


….(ii)


And, After 10 years , the principal is double


Then, Put t = 10 and p = 200 in equation (ii)




Taking log both side, we get



Since, log 2 = 0.6931 (Given)



r = 6.931


Hence, The rate of interest is 6.931%


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on DIfferential CalculusInteractive Quiz on DIfferential CalculusInteractive Quiz on DIfferential Calculus50 mins
Interactive Quiz on Differential Calculus | Check YourselfInteractive Quiz on Differential Calculus | Check YourselfInteractive Quiz on Differential Calculus | Check Yourself56 mins
Functional Equations - JEE with easeFunctional Equations - JEE with easeFunctional Equations - JEE with ease48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses