Step 1 :First, we need to convert the interest rate from percentage to decimal by dividing it by 100. The principal amount \(P\) is \$4363, the amount \(A\) is \$5121, the interest rate \(r\) is 5.2% or 0.052, and the number of times interest is compounded per year \(n\) is 12 (since it's compounded monthly).
Step 2 :We can plug these values into the formula for compound interest and calculate \(t\). The formula is \(t = \frac{\ln(\frac{A}{P})}{n \cdot \ln(1 + \frac{r}{n})}\).
Step 3 :Substituting the given values into the formula, we get \(t = \frac{\ln(\frac{5121}{4363})}{12 \cdot \ln(1 + \frac{0.052}{12})}\).
Step 4 :Calculating the above expression, we get \(t \approx 3.09\).
Step 5 :So, it will take Donnie approximately 3.09 years to accumulate the \$5121.
Step 6 :Final Answer: \(\boxed{3.09}\)