Moneysaver's Bank offers a savings account that earns $3 \%$ interest compounded continuously. If Keith deposits $\$ 2800$, how much will he have in the acco after four years, assuming he makes no withdrawals?
Do not round any intermediate computations, and round your answer to the nearest cent.

Step 1 ：Given that Moneysaver's Bank offers a savings account that earns $3 \%$ interest compounded continuously. Keith deposits $2800 and we need to find how much he will have in the account after four years, assuming he makes no withdrawals.

Step 2 ：We use the formula for continuous compound interest which is \(A = P * e^{rt}\), where:

Step 3 ：\(A\) is the amount of money accumulated after n years, including interest.

Step 4 ：\(P\) is the principal amount (the initial amount of money).

Step 5 ：\(r\) is the annual interest rate (in decimal).

Step 6 ：\(t\) is the time the money is invested for, in years.

Step 7 ：In this case, \(P = \$2800\), \(r = 3\% = 0.03\), and \(t = 4\) years. We need to find \(A\).

Step 8 ：Substituting the given values into the formula, we get \(A = 2800 * e^{0.03*4}\)

Step 9 ：Solving the above expression, we get \(A = 3156.991184422252\)

Step 10 ：Rounding to the nearest cent, we get \(A = \$3156.99\)

Step 11 ：Final Answer: Keith will have approximately \(\boxed{\$3156.99}\) in his account after four years.