The Adeeva's gross monthly income is $ 7800. They have 18 remaining payments of $ 210 on a new car. They are applying for a $15-year, $ 205,000 mortgage at 7.0%. The taxes and insurance on the house are $ 380 per month. The bank will only approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners' insurance that is less than or equal to 28% of their adjusted monthly income. Complete parts (a) through (c) below.
Click the icon to view the table of monthly payments.
a) Determine 28% of the Adeeva's adjusted monthly incomesquare (Round to the nearest cent)
b) Determine the Adeeva's total monthly mortgage payment, including principal, interest, taxes, and homeowners' insurance.

Step 1 ：Calculate 28% of the Adeeva's adjusted monthly income by multiplying their gross monthly income by 0.28: \(0.28 \times 7800 = 2184\)

Step 2 ：The 28% of the Adeeva's adjusted monthly income is \(\boxed{2184}\) dollars

Step 3 ：Calculate the monthly mortgage payment for the principal and interest using the formula: \(M = P[r(1+r)^n]/[(1+r)^n – 1]\) where M is the monthly payment, P is the principal loan amount, r is the monthly interest rate, and n is the number of payments

Step 4 ：Substitute the given values into the formula: \(M = 205000[0.00583(1+0.00583)^{180}]/[(1+0.00583)^{180} – 1]\)

Step 5 ：The monthly mortgage payment for the principal and interest is approximately \(\boxed{1836.51}\) dollars

Step 6 ：Calculate the Adeeva's total monthly mortgage payment by adding the monthly taxes and insurance to the monthly mortgage payment for the principal and interest: \(1836.51 + 380 = 2216.51\)

Step 7 ：The Adeeva's total monthly mortgage payment, including principal, interest, taxes, and homeowners' insurance, is \(\boxed{2216.51}\) dollars