Use $A=P\left(1+\frac{r}{n}\right)^{n t}$ where: $A$ = the amortized amount (total loan/investment amount over the life of the loan/investment) $P=$ the initial amount of the loan/investment $r=$ the annual rate of interest $n=$ the number of times interest is compounded each year $t=$ the time in years Find how long it takes $\$ 1,500.00$ to double if it is invested at $8 \%$ compounded quarterly. It will take years. (Round answer to 3 decimal places.)

Step 1 ：We are given that \(A = 2P\), \(P = 1500\), \(r = 0.08\), and \(n = 4\). We need to find \(t\).

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

Step 3 ：We can substitute the given values into the formula and calculate \(t\).

Step 4 ：Given: \[P = 1500, A = 3000, r = 0.08, n = 4\]

Step 5 ：Substituting these values into the formula, we get: \[t = \frac{\log\left(\frac{3000}{1500}\right)}{4 \log\left(1+\frac{0.08}{4}\right)}\]

Step 6 ：Calculating the above expression, we get: \[t = 8.750697195286625\]

Step 7 ：Rounding to three decimal places, we get: \[t = 8.751\]

Step 8 ：Final Answer: It will take approximately \(\boxed{8.751}\) years for the investment to double.