yessica is buying an apartment for $188,000. she has no down payment. her interest rate is 3.5%, a property tax of $936 a year, and she is doing a 15-year mortgage. what will the total interest be? put pmi as 0.5% and property insurance as $1,000 per year.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mortgage Calculation" ], "new_concepts": [ "Amortization Interest" ], "current_concepts": [ "Mortgage Calculation", "Amortization Interest" ] } ## Calculate the monthly principal and interest payment $$ \begin{aligned} P &= 188000 \ r &= \frac{0.035}{12} \approx 0.00291667 \ n &= 15 \times 12 = 180 \ M &= P \frac{r(1+r)^n}{(1+r)^n - 1} \ M &= 188000 \frac{0.00291667(1.00291667)^{180}}{(1.00291667)^{180} - 1} \approx 1344.89 \end{aligned} $$ ## Calculate the total amount paid for principal and interest $$ \begin{aligned} \text{Total Payments} &= M \times n \ \text{Total Payments} &= 1344.89 \times 180 = 242080.20 \end{aligned} $$ ## Calculate the total interest paid $$ \begin{aligned} \text{Total Interest} &= \text{Total Payments} - P \ \text{Total Interest} &= 242080.20 - 188000 = 54080.20 \end{aligned} $$ $\$54,080.20$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Algebra", "Mortgage Calculation" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the monthly principal and interest payment

Calculate the total amount paid for principal and interest

Calculate the total interest paid

Answer: