What constant interest rate is required if an initial deposit placed into an account accrues interest compounded continuously is to double its value in six years? `(ln|x|=0. 6930)`

Explanation

The balance N(t) in the account at any time t,
`(dN)/(dt)-kN=0`, its solution is `N(t) = ce^(kt)`………..(1)
Let initial deposit be `N_(0)`.
At t=0, `N(0)=N_(0)` which when substituted into equation `N_(0)=ce^(k(0))=c`
and equation (1) becomes `N(t) = N_(0)e^(kt)`.
We seek the value of k for which `N=2N_(0)` when t=6, substituting these values into (2) and solving for k we find `2N_(0)=N_(0)e^(k(6))`.
or `e^(6k)=2` or `k=1/6In|2|=0.1155` An interest rate of `11.55` percent is required.