jacob is buying a house for \$435,600. he has a down payment of \$30,000. his interest rate is 2.88%, property tax is \$2,800, the pmi is 0.5% and the property insurance is \$1,200 per year. he is using a 30 year mortgage. how much will his monthly payment be?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mortgage Calculation", "PITI Payment", "Private Mortgage Insurance", "30-Year Fixed Mortgage" ], "new_concepts": [], "current_concepts": [ "Mortgage Calculation", "PITI Payment", "Private Mortgage Insurance", "30-Year Fixed Mortgage" ] } ## Calculate the loan principal and monthly interest rate $$ \begin{aligned} P &= 435,600 - 30,000 = 405,600 \ r &= \frac{0.0288}{12} = 0.0024 \ n &= 30 \times 12 = 360 \end{aligned} $$ ## Calculate the monthly principal and interest (P&I) payment $$ \begin{aligned} M_{PI} &= P \times \frac{r(1+r)^n}{(1+r)^n - 1} \ M_{PI} &= 405,600 \times \frac{0.0024(1.0024)^{360}}{(1.0024)^{360} - 1} \ M_{PI} &\approx 405,600 \times 0.00415166 \approx 1,683.91 \end{aligned} $$ ## Calculate monthly taxes, insurance, and PMI to find the total monthly payment $$ \begin{aligned} \text{Monthly Tax} &= \frac{2,800}{12} \approx 233.33 \ \text{Monthly Insurance} &= \frac{1,200}{12} = 100.00 \ \text{Monthly PMI} &= \frac{405,600 \times 0.005}{12} = 169.00 \ \text{Total Monthly Payment} &= 1,683.91 + 233.33 + 100.00 + 169.00 = 2,186.24 \end{aligned} $$ $2,186.24$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Mortgage Calculation" ] }

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Explanation:

Calculate the loan principal and monthly interest rate

Calculate the monthly principal and interest (P&I) payment

Calculate monthly taxes, insurance, and PMI to find the total monthly payment

Answer: