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.

  • 2
    $\begingroup$ 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? $\endgroup$ – TravisJ Apr 11 '15 at 1:26

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:

$$i \approx 5.87\%$$

| cite | improve this answer | |
  • $\begingroup$ It would be better to say multiply by $100\%$ so that your final answer is $i \approx 5.87\%$. $\endgroup$ – N. F. Taussig Apr 11 '15 at 11:43
  • $\begingroup$ I tried putting a percent symbol but somehow it disappeared. Is there a Tex symbol for it? $\endgroup$ – Shrey Apr 11 '15 at 15:20
  • $\begingroup$ In LaTeX, you have to type \% to obtain a $\%$ symbol. $\endgroup$ – N. F. Taussig Apr 11 '15 at 22:58

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