Question 2 of 9
This quiz: 9 point(s
This question: 1 p
Use the formula for compound interest to find the compound amount and the interest. Interest is compounded quarterly.
\begin{tabular}{|c|c|c|}
\hline Principal & Rate of Interest & Time \\
\hline$\$ 18,000$ & $10 \%$ & $3 \frac{1}{2}$ years \\
\hline
\end{tabular}

What is the compound amount?
$\$ \square$ (Round to the nearest cent.)
What is the amount of compound interest?
$\$ \square$ (Round to the nearest cent.)

Step 1 ：Given the principal amount \(P = \$18,000\), the annual interest rate \(r = 10\% = 0.10\), the number of times that interest is compounded per year \(n = 4\) (since interest is compounded quarterly), and the time the money is invested for \(t = 3.5\) years.

Step 2 ：We use the formula for compound interest \(A = P(1 + r/n)^{nt}\), where \(A\) is the amount of money accumulated after \(n\) years, including interest.

Step 3 ：Substitute the given values into the formula to find the compound amount: \(A = 18000(1 + 0.1/4)^{4*3.5} \approx \$25433.53\).

Step 4 ：To find the amount of compound interest, subtract the principal from the compound amount: \(interest = 25433.53 - 18000 \approx \$7433.53\).

Step 5 ：Final Answer: The compound amount is \(\boxed{\$25433.53}\) and the compound interest is \(\boxed{\$7433.53}\).