Question

If an account that earns interest compounded continuously takes 37 years to double in value, how long will it take to triple in value?

Here's what I think...I divided 37 with 2 and multiplied that value with 3 and so my answer is 55.5 years. Am I correct? If not, please help me get the right answer! Thanks in advance.

Answer 1

continuous growth is given by the exponential equation
y = a(e)^kt
let a=1 then for doubling y = 2

2 = e^37k
37k = ln 2
k = ln 2/37

so y = a(e)^(ln2/37)t

so now you want y to be 3

3 = e^(ln2/37)t

(ln2/37)t = ln3
t = 37ln3/ln2 = 58.6 years

You titled your post "exponential" but totally ignored that important property.
You treated the relationship as "linear"

Answer 2

thanks! this tells me i need to review the chapter...

Answer 3

921