QuestionJuly 10, 2025

Use the mortgage calculator in the window you opened at the beginning of this activity to calculate the following: 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. a. 821,424.53 b. 691,124.24 c. 541,493.70 d. 763,546.45

Use the mortgage calculator in the window you opened at the beginning of this activity to calculate the following: 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. a. 821,424.53 b. 691,124.24 c. 541,493.70 d. 763,546.45
Use the mortgage calculator in the window you opened at the beginning of this activity to calculate the following: 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. a. 821,424.53 b. 691,124.24 c. 541,493.70 d. 763,546.45

Solution
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Answer

None of the provided options match the calculated total cost of \ 803,090.40. Explanation 1. Calculate Loan Amount Subtract down payment from house price: 377,500 - 27,500 = 350,000. 2. Calculate Monthly Interest Rate Convert annual interest rate to monthly: \frac{4.75}{100 \times 12} = 0.0039583. 3. Calculate Monthly Mortgage Payment Use formula: M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} where P = 350,000, r = 0.0039583, n = 360. Calculate M: M = \frac{350,000 \times 0.0039583 \times (1 + 0.0039583)^{360}}{(1 + 0.0039583)^{360} - 1} \approx 1826.64. 4. Calculate Total Property Tax and Insurance Costs Annual property tax: 2,100. Annual insurance: 1,000. Total for 30 years: (2,100 + 1,000) \times 30 = 93,000. 5. Calculate PMI Cost PMI is 0.5\% of loan amount per year: 350,000 \times 0.005 = 1,750. Total for 30 years: 1,750 \times 30 = 52,500. 6. Calculate Total Cost Over 360 Payments Total mortgage payments: 1826.64 \times 360 = 657,590.40. Add taxes, insurance, and PMI: 657,590.40 + 93,000 + 52,500 = 803,090.40.

Explanation

1. Calculate Loan Amount<br /> Subtract down payment from house price: $377,500 - 27,500 = 350,000$.<br />2. Calculate Monthly Interest Rate<br /> Convert annual interest rate to monthly: $\frac{4.75}{100 \times 12} = 0.0039583$.<br />3. Calculate Monthly Mortgage Payment<br /> Use formula: $M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$ where $P = 350,000$, $r = 0.0039583$, $n = 360$. <br /> Calculate $M$: $M = \frac{350,000 \times 0.0039583 \times (1 + 0.0039583)^{360}}{(1 + 0.0039583)^{360} - 1} \approx 1826.64$.<br />4. Calculate Total Property Tax and Insurance Costs<br /> Annual property tax: $2,100$. Annual insurance: $1,000$. Total for 30 years: $(2,100 + 1,000) \times 30 = 93,000$.<br />5. Calculate PMI Cost<br /> PMI is $0.5\%$ of loan amount per year: $350,000 \times 0.005 = 1,750$. Total for 30 years: $1,750 \times 30 = 52,500$.<br />6. Calculate Total Cost Over 360 Payments<br /> Total mortgage payments: $1826.64 \times 360 = 657,590.40$. Add taxes, insurance, and PMI: $657,590.40 + 93,000 + 52,500 = 803,090.40$.
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