Finding the monthly payment, total payment, and interest for a loan
When Tammy bought her condominium, she got her mortgage through her credit union.
The mortgage was a personal, amortized loan for $\$ 92,000$, at an interest rate of $3.3 \%$, with monthly payments for a term of 25 years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find Tammy's monthly payment.
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(b) If Tammy pays the monthly payment each month for the full term, find her total amount to repay the loan.
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(c) If Tammy pays the monthly payment each month for the full term, find the total amount of interest she will pay.
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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 \(\boxed{43229.39}\).