bob is buying a house for \$377,500. he has a down payment of \$27,500. his interest rate is 4.75\%, a property tax of \$2,100 a year, and he is doing a 30-year mortgage. what will his total cost over 360 payments be? put pmi as 0.5\% and property insurance as \$1,000 per year.

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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" ], "new_concepts": [], "current_concepts": [ "Mortgage Calculation", "PITI Payment", "Private Mortgage Insurance" ] } ## Calculate loan principal and monthly mortgage payment $$ \begin{aligned} P &= 377500 - 27500 = 350000 \ r &= \frac{0.0475}{12} \approx 0.00395833 \ n &= 360 \ M &= P \frac{r(1+r)^n}{(1+r)^n - 1} \ M &= 350000 \frac{0.00395833(1.00395833)^{360}}{(1.00395833)^{360} - 1} \approx 1825.83 \end{aligned} $$ ## Calculate monthly escrow costs (Taxes, Insurance, and PMI) $$ \begin{aligned} \text{Monthly Tax} &= \frac{2100}{12} = 175.00 \ \text{Monthly Home Insurance} &= \frac{1000}{12} \approx 83.33 \ \text{Down Payment \%} &= \frac{27500}{377500} \approx 7.28\% \quad (< 20\%, \text{ so PMI applies}) \ \text{Annual PMI} &= 350000 \times 0.005 = 1750 \ \text{Monthly PMI} &= \frac{1750}{12} \approx 145.83 \end{aligned} $$ ## Calculate total monthly payment and total cost over 360 payments $$ \begin{aligned} \text{Total Monthly PITI + PMI} &= 1825.83 + 175.00 + 83.33 + 145.83 = 2229.99 \ \text{Total Cost over 360 payments} &= 2229.99 \times 360 = 802796.40 \end{aligned} $$ $s = \$802,796.40$ (or approximately $\$802,800$ depending on rounding methods used for intermediate monthly values) { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Mortgage Calculation" ] }

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Explanation:

Calculate loan principal and monthly mortgage payment

Calculate monthly escrow costs (Taxes, Insurance, and PMI)

Calculate total monthly payment and total cost over 360 payments

Answer: