Question

Suppose that $2300 is initially invested in an account at a fixed interest rate, compounded continuously. Suppose also that, after two years, the amount of money in the account is $2519. Find the interest rate per year.

Answer 1

The formula for compound continuously rate
`A = P e^(rt)`.
Where is A (future amount) = 2519, P (initial amount) = 2300, e is the mathematical constant, r (rate of interest) which is unknown, and t (time in years) = 20

Now we plug in the variables into the equation.


`2519 = 2300 e^(r*20)`

It is asking for the rate, so must isolate
`r`.

First we divide 2300 on both sides of the equation.


`(2519)/(2300) = (2300)/(2300) e^(r*20)`

`1.0952 = e^((r*20))`

Then we enter the inverse of
`e`, which is log.


`log(1.0952)=log(e^(r*20))`

`0.0395=20r * log(e)`

Then divide
`log(e)` on both sides.


`(0.0395)/(log(e)) =20r * (log(e))/(log(e))`

`(0.0395)/(log(e)) =20r`

Then divide 20 on both sides.


`(0.0395)/(20*log(e)) = (20r)/(20)`

`(0.0395)/(20*log(e)) = r`

Finally solve for
`r`

0 = r

The answer is r = 0%