sierra is buying an apartment for \$199,800. she has a down payment of \$15,000. her interest rate is 7.25\%, property tax is \$630, the pmi is 0.5\% and the property insurance is \$1,000 per year. she is using a 15 year mortgage. how much will she pay in total interest over the life of the loan?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mortgage Calculation" ], "new_concepts": [ "15-Year Fixed Mortgage" ], "current_concepts": [ "Mortgage Calculation", "15-Year Fixed Mortgage", "Amortization Interest" ] } ## Calculate the loan principal $$ P = \$199,800 - \$15,000 = \$184,800 $$ ## Calculate the monthly payment $$ \begin{aligned} r &= \frac{0.0725}{12} \approx 0.006041667 \ n &= 15 \times 12 = 180 \ M &= P \frac{r(1+r)^n}{(1+r)^n - 1} \ M &= 184,800 \frac{0.006041667(1.006041667)^{180}}{(1.006041667)^{180} - 1} \approx \$1,682.16 \end{aligned} $$ ## Calculate the total interest paid $$ \begin{aligned} \text{Total Payments} &= 180 \times \$1,682.16 = \$302,788.80 \ \text{Total Interest} &= \text{Total Payments} - P \ \text{Total Interest} &= \$302,788.80 - \$184,800 = \$117,988.80 \end{aligned} $$ $117,988.80$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Mortgage Calculation" ] }

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Calculate the loan principal

Calculate the monthly payment

Calculate the total interest paid

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