Step 1 :Given that the principal amount (P) is $16,000, the annual interest rate (r) is 6% or 0.06, the interest is compounded quarterly so n = 4, and the money is invested for 5 years (t).
Step 2 :The formula for compound interest is \(A = P (1 + r/n)^{nt}\), where A is the amount of money accumulated after n years, including interest.
Step 3 :Substitute the given values into the formula: \(A = 16000 (1 + 0.06/4)^{4*5}\)
Step 4 :First, calculate the value inside the brackets: \(1 + 0.06/4 = 1.015\)
Step 5 :Then, raise this to the power of 20 (4*5): \((1.015)^{20} \approx 1.346855007\)
Step 6 :Finally, multiply this by the principal amount: \(16000 * 1.346855007 \approx 21549.68\)
Step 7 :\(\boxed{21549.68}\) is the final amount in the account after 5 years with quarterly compounding, rounded to the nearest cent.