Step 1 :Given that Tammy's principal loan amount (P) is $92,000, the annual interest rate (r_annual) is 3.3%, and the term of the loan (n_years) is 25 years.
Step 2 :First, we need to convert the annual interest rate to a monthly interest rate (r) by dividing it by 12. So, \(r = \frac{0.033}{12} = 0.00275\).
Step 3 :Next, we need to convert the term of the loan from years to months (n) by multiplying it by 12. So, \(n = 25 \times 12 = 300\) months.
Step 4 :We can now calculate Tammy's monthly payment (M) using the formula for an amortized loan: \[M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}\]. Substituting the given values, we get \(M = 92000 \frac{0.00275(1 + 0.00275)^{300}}{(1 + 0.00275)^{300} - 1} = 450.76464125878135\).
Step 5 :Rounding to the nearest cent, Tammy's monthly payment is \(\boxed{450.76}\).
Step 6 :To find the total amount to repay the loan, we multiply the monthly payment by the number of payments: \(M \times n = 450.76464125878135 \times 300 = 135229.39237763442\).
Step 7 :Rounding to the nearest cent, the total amount to repay the loan is \(\boxed{135229.39}\).
Step 8 :To find the total amount of interest paid, we subtract the principal loan amount from the total amount repaid: \(135229.39237763442 - 92000 = 43229.392377634416\).
Step 9 :Rounding to the nearest cent, the total amount of interest Tammy will pay is \(\boxed{43229.39}\).