Question
Meg invested $\$ 16,000$ in a savings account. If the annual interest rate is $6 \%$, how much will be in the account in 5 year with quarterly compounding?

Round your answer to the nearest cent.
DO NOT round until you calculate the final answer

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.