Compound Interest

[MaggieSmith12345]

Hello,

So the question is suppose you have $32,000 to invest and you want it to double in 8 years. At what rate of interest would have have to invest if it was compounded a) quarterly b) continuously

so! I plugged all my given values into the formula A=P(1+R)^n knowing that I was solving for R . But then I got stuck

64,000=32,000[1+(r/4)]^(8)(4)

so then i divided the 64,000 by 32,000 to get 2=[1+(r/4)]^32

im not entirely positive how to approach from there.. would I get the 32nd root of 2 then proceed?

Thanks!

 

[BigGlenntheHeavy]

\(\displaystyle Compounded \ Quarterly: \ A \ = \ P\bigg(1+\frac{r}{4}\bigg)^{4t}.\)

\(\displaystyle Compounded \ Continuously: \ A \ = \ Pe^{rt}.\)

\(\displaystyle Note: \ Since \ you \ want \ to \ double \ your \ investment \ in \ 8 \ years, \ the \ \$32,000 \ is \ a \ red\)

\(\displaystyle herring \ since \ all \ you \ want \ to \ know \ is \ what \ interest \ you \ must \ derive.\)