QuestionMay 19, 2026

7. The bank offered Annette a 380,000 30-year mortgage at 3.54% She is deciding whether to purchase 2 points to reduce her APR by 0.25% per point. Each point will cost 1% of the loan value. a. Calculate her monthly payments with the points. b. Calculate her monthly payments without the points. c. Determine the breakeven month.

7. The bank offered Annette a 380,000 30-year mortgage at 3.54% She is deciding whether to purchase 2 points to reduce her APR by 0.25% per point. Each point will cost 1% of the loan value. a. Calculate her monthly payments with the points. b. Calculate her monthly payments without the points. c. Determine the breakeven month.
7. The bank offered Annette a 380,000 30-year mortgage at 3.54% She is deciding whether to purchase 2 points to reduce her APR by 0.25% per point. Each point will cost 1% of the loan value. a. Calculate her monthly payments with the points. b. Calculate her monthly payments without the points. c. Determine the breakeven month.

Solution
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Answer

a. 1613.37 ### b. 1708.74 ### c. 80 months Explanation 1. Calculate new interest rate with points Each point reduces APR by 0.25\%; 2 points reduce by 0.50\%. Original rate 3.54\%, so new rate = 3.54\% - 0.50\% = 3.04\%. 2. Calculate monthly payment formula Use **M = P \frac{r(1+r)^n}{(1+r)^n - 1}** where P=loan, r=monthly rate, n=months. For points: P = 380000, r = 0.0304/12 \approx 0.0025333, n = 360. M = 380000 \cdot \frac{0.0025333(1.0025333)^{360}}{(1.0025333)^{360} - 1} \approx 1613.37. 3. Calculate monthly payment without points r = 0.0354/12 \approx 0.00295. M = 380000 \cdot \frac{0.00295(1.00295)^{360}}{(1.00295)^{360} - 1} \approx 1708.74. 4. Calculate total cost of points Each point costs 1\% of loan: 0.01 \cdot 380000 = 3800. Two points = 7600. 5. Determine breakeven month Monthly savings = 1708.74 - 1613.37 \approx 95.37. Breakeven month = 7600 / 95.37 \approx 79.68 \approx 80 months.

Explanation

1. Calculate new interest rate with points <br /> Each point reduces APR by $0.25\%$; $2$ points reduce by $0.50\%$. Original rate $3.54\%$, so new rate $= 3.54\% - 0.50\% = 3.04\%$.<br /><br />2. Calculate monthly payment formula <br /> Use **$M = P \frac{r(1+r)^n}{(1+r)^n - 1}$** where $P$=loan, $r$=monthly rate, $n$=months. <br />For points: <br />$P = 380000$, $r = 0.0304/12 \approx 0.0025333$, $n = 360$. <br />$M = 380000 \cdot \frac{0.0025333(1.0025333)^{360}}{(1.0025333)^{360} - 1} \approx 1613.37$.<br /><br />3. Calculate monthly payment without points <br /> $r = 0.0354/12 \approx 0.00295$. <br />$M = 380000 \cdot \frac{0.00295(1.00295)^{360}}{(1.00295)^{360} - 1} \approx 1708.74$.<br /><br />4. Calculate total cost of points <br /> Each point costs $1\%$ of loan: $0.01 \cdot 380000 = 3800$. <br />Two points = $7600$.<br /><br />5. Determine breakeven month <br /> Monthly savings = $1708.74 - 1613.37 \approx 95.37$. <br />Breakeven month $= 7600 / 95.37 \approx 79.68 \approx 80$ months.
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