How long will it take $\$ 5,000$ to grow to $\$ 9,000$ if it is invested at $7 \%$ compounded monthly?
years (Round to the nearest tenth of a year.)

Step 1 ：We are given that the principal amount (P) is $5,000, the final amount (A) is $9,000, the annual interest rate (r) is 7% or 0.07 in decimal form, and the interest is compounded monthly which means it is compounded 12 times a year (n=12). We need to find the time (t) in years it will take for the principal amount to grow to the final amount.

Step 2 ：We can use the formula for compound interest which is \(A = P(1 + \frac{r}{n})^{nt}\).

Step 3 ：We rearrange the formula to solve for t, which gives us \(t = \frac{\log(\frac{A}{P})}{n \cdot \log(1 + \frac{r}{n})}\).

Step 4 ：Substituting the given values into the formula, we get \(t = \frac{\log(\frac{9000}{5000})}{12 \cdot \log(1 + \frac{0.07}{12})}\).

Step 5 ：Solving the above expression, we find that t is approximately 8.4.

Step 6 ：So, it will take approximately \(\boxed{8.4}\) years for $5,000 to grow to $9,000 if it is invested at 7% compounded monthly.