Use the formula $A=P\left(1+\frac{r}{n}\right)^{n t}$ to solve the compound interest problem. Find how long it takes for $\$ 1700$ to double if it is invested at $3 \%$ interest compounded monthly. The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Step 1 ：We are given the principal amount (P) as $1700, the rate (r) as $3\%$ or $0.03$, and the number of times interest applied per time period (n) as $12$ (since it's compounded monthly). We are also given that the final amount (A) is double the principal, so $A = 2 * P = 2 * 1700 = 3400$. We need to find the time (t) it takes for the money to double.

Step 2 ：We can rearrange the formula $A=P\left(1+\frac{r}{n}\right)^{n t}$ to solve for t: $t = \frac{\log\left(\frac{A}{P}\right)}{n \log\left(1+\frac{r}{n}\right)}$

Step 3 ：We can plug in the given values into this formula to find the time it takes for the money to double. Where P = 1700, A = 3400, r = 0.03, and n = 12.

Step 4 ：By substituting the values into the formula, we get t = 23.13377513240193

Step 5 ：Rounding to the nearest tenth, we get \(\boxed{23.1}\) years.