Problem
Exponential and Logarithmic Functions Finding the final amount in a word problem on continuous compound... Moneysaver's Bank offers a savings account that earns 3\% interest per year, compounded continuously. If Shen dep $\$ 3200$, how much will he have in the account after four years, assuming he makes no withdrawals? Do not round any intermediate computations, and round your answer to the nearest cent. Explanation Check
Solution
Step 1 ：Given that the principal amount (P) is $3200, the annual interest rate (r) is 3% or 0.03 in decimal form, and the time (t) is 4 years.
Step 2 ：We can use the formula for continuous compounding, which is \(A = Pe^{rt}\), where A is the final amount.
Step 3 ：Substitute the given values into the formula: \(A = 3200 \cdot e^{0.03 \cdot 4}\).
Step 4 ：Calculate the final amount A.
Step 5 ：The final amount in the account after four years will be \(\boxed{3607.99}\).
