How long will it take an investment to double in value if the interest rate is 11% compounded continuoulsy and what is the equivalent annual interest rate?
The best way to approach this is to use the traditional continuous compound interest formula:
`A(t) = A_0 e^(rt)`
Here, `A(t)` is the amount after a given amount of time, `A_0` is the initial amount you invest, `r` is the interest rate (11%), and `t` is the time in years.
Let's answer the first part, where we calculate the amount of time that is needed for the investment to double. In other words, we want to find when `A(t)` would be `2A_0`. So, let's substitute our given value of `r` and our value for `A(t)` into the continuous compound interest formula:
`2A_0 = A_0e^(0.11t)`
The problem asks us to solve for the amount of time, so let's go ahead and do that now. Start by dividing both...
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