Here is the question: Noha is investing ${$}2517$ in an account compounded monthly. She wants to have ${$}3000$ in $3$ years for a trip to Europe. What interest rate, to the nearest hundredth of a percent, compounded monthly, does she need?
I know that I need to use the formula $A=P(1+i)^{n}$
Here is how I substituted all my given values: $3000=2517[1+ (i/12)]^{36}$
I need assistance on how to find the interest rate, we never learned how to do that in class.
You're on the right track.
$$\frac{3000}{2517} = (1 + \frac{i}{12})^{36}$$ $$ \sqrt[36]{\frac {3000}{2517}} = (1 + \frac{i}{12}) $$ $$1.0048 \approx 1 + \frac{i}{12}$$ $$0.0048 \approx \frac{i}{12}$$ $$0.0587 \approx i$$
Then, multiply by 100 to get the percentage value:
$$i \approx 5.87\%$$