Step 1 :Given values are total amount paid \(A = \$99000\), annual interest rate \(r = 3\% = 0.03\), number of times interest is compounded per year \(n = 12\), and time in years \(t = 30\).
Step 2 :We need to calculate the principal amount \(P\).
Step 3 :The formula to calculate the principal amount is \(P = \frac{A}{(1 + \frac{r}{n})^{nt}}\).
Step 4 :Substitute the given values into the formula: \(P = \frac{99000}{(1 + \frac{0.03}{12})^{12*30}}\).
Step 5 :Solving the above expression gives \(P = 40295.62807769027\).
Step 6 :Round the principal amount to the nearest cent to get the final answer.
Step 7 :Final Answer: The principal amount of the loan was approximately \(\boxed{\$40295.63}\).