Q. 55.0( 1 Vote )

If the interest is compounded continuously at 6% per annum, how much worth ₹ 1000 will be after ten years? How long will it take to double ₹ 1000?

[Given e0.6 = 1.822]

Answer :

Let the principal, rate and time be Rs P, r and t years.

Also, let the initial principal be Po.




Integrating both sides, we have


∫dt


log|P| = t + c ……(1)


Now, at t = 0, P = Po


log| Po | = 0 + c


c = log| Po |……(2)


Putting the value of c in equation (1) we have,


log|P| = t + log|Po|


log|P| – log|Po| = t


(log |P| – log|Po|) = t []


log ( = t ……(3)


Now, Po = 1000, t = 10years, r = 6


log ( = ×10


log ( = 0.6



P = ×1000


P = 1.822×1000 (Given: = 1.822)


P = 1822


Rs 1000 will be Rs 1822 after 10 years at 6% rate.


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