A loan is paid off in 30 years with a total of $\$ 99,000$. It had a $3 \%$ interest rate that compounded monthly.
What was the principat?

Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.

Provideyour answer below:

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 \(\boxed{\$40295.63}\).