# Issue with Compound Interest

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 can solve the equation by first dividing by 2517 (both sides) then taking the 36th root of both sides. That'll leave you with # = 1 + i/12 which hopefully you can solve? – TravisJ Apr 11 '15 at 1:26

$$\frac{3000}{2517} = (1 + \frac{i}{12})^{36}$$ $$\sqrt[36]{\frac {3000}{2517}} = (1 + \frac{i}{12})$$ $$1.0048 \approx 1 + \frac{i}{12}$$ $$0.0048 \approx \frac{i}{12}$$ $$0.0587 \approx i$$
$$i \approx 5.87\%$$
• It would be better to say multiply by $100\%$ so that your final answer is $i \approx 5.87\%$. – N. F. Taussig Apr 11 '15 at 11:43
• In LaTeX, you have to type \% to obtain a $\%$ symbol. – N. F. Taussig Apr 11 '15 at 22:58