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.