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What constant interest rate is required ...

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)`

Text Solution

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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.
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