Step 1 :Given that the principal amount (P) is $5000, the annual interest rate (r) is 7% or 0.07, the number of times that interest is compounded per year (n) is 12, and the time the money is invested for in years (t) is 10.
Step 2 :The formula for compound interest is \(A = P (1 + \frac{r}{n})^{nt}\)
Step 3 :Substitute the given values into the formula: \(A = 5000 (1 + \frac{0.07}{12})^{12*10}\)
Step 4 :Simplify the expression inside the parentheses: \(A = 5000 (1 + 0.0058333333)^{120}\)
Step 5 :Calculate the power: \(A = 5000 * 2.00968307\)
Step 6 :Multiply to find the final amount: \(A = \boxed{10048.42}\)