# How do you find the required annual interest rate, to the nearest tenth of a percent, for $898 to grow to$1511 if interest is compounded monthly for 2 years?

Oct 17, 2015

Set up equation, then solve for i.

#### Explanation:

$898 {\left(1 + \frac{i}{12}\right)}^{12 \cdot 2} = 1511$

${\left(1 + \frac{i}{12}\right)}^{24} = \frac{1511}{898}$

Now exponentiate each side of the equation by $\frac{1}{24}$

${\left[{\left(1 + \frac{i}{12}\right)}^{24}\right]}^{\frac{1}{24}} = {\left(\frac{1511}{898}\right)}^{\frac{1}{24}}$

$\left(1 + \frac{i}{12}\right) = {\left(\frac{1511}{898}\right)}^{\frac{1}{24}}$

Now solve for i:

i=[(1511/898)^(1/24) -1]*12=0.263 or 26.3%

hope that helped