the house is selling for $285,500 and has a property tax of $952. brooke has a down payment of $40,000. her interest rate is 6.25%, pmi is 0.5% and the property insurance is $850 per year. she is getting a 30 year mortgage.
the house is selling for $285,500 and has a property tax of $952. isaac has no down payment. his interest rate is 6.25%, pmi is 0.5% and the property insurance is $850 per year. he is getting a 15 year mortgage.
a. brooke
b. isaac

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mortgage Calculation", "PITI Payment", "Private Mortgage Insurance", "30-Year Fixed Mortgage", "15-Year Fixed Mortgage" ], "new_concepts": [], "current_concepts": [ "Mortgage Calculation", "PITI Payment", "Private Mortgage Insurance", "30-Year Fixed Mortgage", "15-Year Fixed Mortgage" ] } ## Calculate monthly PITI for Brooke $$ \begin{aligned} &\text{Loan Amount } (P_B) = 285,500 - 40,000 = 245,500 \ &\text{Monthly Interest Rate } (r) = \frac{0.0625}{12} \approx 0.00520833 \ &\text{Number of Payments } (n_B) = 30 \times 12 = 360 \ &\text{Monthly Principal \& Interest } (M_B) = P_B \times \frac{r(1+r)^{n_B}}{(1+r)^{n_B}-1} \approx 245,500 \times 0.00615717 \approx 1,511.59 \ &\text{Monthly Property Tax} = \frac{952}{12} \approx 79.33 \ &\text{Monthly Property Insurance} = \frac{850}{12} \approx 70.83 \ &\text{Monthly PMI } (\text{since down payment } < 20\%) = \frac{245,500 \times 0.005}{12} \approx 102.29 \ &\text{Total Monthly PITI}_B = 1,511.59 + 79.33 + 70.83 + 102.29 = 1,764.04 \end{aligned} $$ ## Calculate monthly PITI for Isaac $$ \begin{aligned} &\text{Loan Amount } (P_I) = 285,500 \ &\text{Number of Payments } (n_I) = 15 \times 12 = 180 \ &\text{Monthly Principal \& Interest } (M_I) = P_I \times \frac{r(1+r)^{n_I}}{(1+r)^{n_I}-1} \approx 285,500 \times 0.00857421 \approx 2,447.94 \ &\text{Monthly Property Tax} = \frac{952}{12} \approx 79.33 \ &\text{Monthly Property Insurance} = \frac{850}{12} \approx 70.83 \ &\text{Monthly PMI } (\text{since down payment } < 20\%) = \frac{285,500 \times 0.005}{12} \approx 118.96 \ &\text{Total Monthly PITI}_I = 2,447.94 + 79.33 + 70.83 + 118.96 = 2,717.06 \end{aligned} $$ ## Compare monthly payments $$ \begin{aligned} &\text{Total Monthly PITI}_B \approx 1,764.04 \ &\text{Total Monthly PITI}_I \approx 2,717.06 \ &\text{Total Monthly PITI}_B < \text{Total Monthly PITI}_I \end{aligned} $$

a. Brooke

b. Isaac

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Mortgage Calculation" ] }

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Calculate monthly PITI for Brooke

Calculate monthly PITI for Isaac

Compare monthly payments

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