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]

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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