Question

A person deposit 20000 in a
account which
pays
5% interest
per annum, Compounded Continuously. Find the time required for the account to double in value, presuming no withdrawals and no addition deposit?​

Answer 1

${\boxed {\red {\mathtt{AnSweR}}}}$

GIVEN:-

$⬇⬇$

DEPOSITED AMOUNT (P) = Rs. 20,000

Rate of interest (R) = 5%

in Question it is given that amount is DOUBLED so,

AMOUNT = 2(20,000) = Rs.40,000

FIND:-

$⬇⬇$

TIME (t)=?

SOLUTION:-

WE KNOW THE FORMULA THAT:-

$A = P(1 + \frac{R}{100} {)}^{t}$

$40000 = 20000(1 + \frac{5}{100} {)}^{t}$

$\cancel{40000} = \cancel{20000}(1 + \frac{5}{100} {)}^{t}$

$2 = ( \frac{100 + 5}{100} {)}^{t}$

$2 = (\frac{105}{100} {)}^{t}$

$2 = ( \frac{21}{20} {)}^{t}$

flip the eq.

$( \frac{21}{20} {)}^{t} = 2$

$log(( \frac{21}{20} {)}^{t} ) = log(2) \: \: \: \: (take \: log \: of \: both \: sides)$

$t \times ( log( \frac{21}{20} ) ) = log(2)$

$t = \frac{ log(2) }{ log( \frac{21}{20} ) }$

$t = 14.206699$

so, time = $\boxed{14.206699}$