A certain loan program offers an interest rate of $5 \%$, compounded continuously. Assuming no payments are made, how much would be owed after four years a loan of $\$ 2600$ ? Do not round any intermediate computations, and round your answer to the nearest cent.

Step 1 ：We are given a loan of $2600 with an interest rate of 5%, compounded continuously. We are asked to find out how much would be owed after four years assuming no payments are made.

Step 2 ：The formula for continuous compound interest is \(A = P * e^{rt}\), where \(A\) is the amount of money accumulated after n years, including interest. \(P\) is the principal amount (the initial amount of money), \(r\) is the annual interest rate (in decimal), and \(t\) is the time the money is invested for in years.

Step 3 ：In this case, \(P = \$2600\), \(r = 5\% = 0.05\), and \(t = 4\) years. We can substitute these values into the formula to find the amount owed after four years.

Step 4 ：Substituting the given values into the formula, we get \(A = 2600 * e^{(0.05*4)}\)

Step 5 ：Solving the above expression, we get \(A = 3175.6471712164416\)

Step 6 ：Rounding to the nearest cent, the amount owed after four years would be approximately \(\boxed{\$3175.65}\)