Problem
An original investment of $\$ 9,000$ earns $6.75 \%$ interest compounded continuously. What will the investment be worth in 3 years? 30 years? After 3 years, the investment will be worth $\$ 11020.14$. (Do not round until the final answer. Then round to the nearest cent as needed.) After 30 years, the investment will be worth $\$ \square$. (Do not round unti the final answer. Then round to the nearest cent as needed.)
Solution
Step 1 ：Use the formula for continuous compounding interest: \( A = P \cdot e^{(rt)} \)
Step 2 ：Substitute the given values: \( P = \$9000 \), \( r = 0.0675 \), \( t = 30 \)
Step 3 ：Calculate the accumulated amount: \( A = 9000 \cdot e^{(0.0675 \cdot 30)} \)
Step 4 ：Round the final answer to the nearest cent
Step 5 ：\( \boxed{\$68185.00} \)
