Mortgage Points worksheet

1. Break-even point (months): 87

1. Cost of the points: each point is 1% of the loan

   $\frac{3}{100}\times \mathrm{\$275,000.00}$$=\mathrm{\$8,250.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{7.5\%}-3\times \mathrm{0.19\%}$$=\mathrm{6.93\%}$

3. Monthly payment at 7.5% over 240 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$275,000.00}\times \frac{0.00625}{\left(1-{\left(1+0.00625\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,215.38}$

4. Monthly payment at 6.93%

   $\mathrm{\$275,000.00}\times \frac{0.005775}{\left(1-{\left(1+0.005775\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,120.53}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,215.38}-\mathrm{\$2,120.53}$$=\mathrm{\$94.85}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$8,250.00}}{\mathrm{\$94.85}}$$=86.9806$

7. Net benefit after 108 months: payment savings, plus the lower balance still owed ($195,486.94 instead of $198,724.46), minus the points cost

   $108\times \mathrm{\$94.85}+\mathrm{\$3,237.52}-\mathrm{\$8,250.00}$$=\mathrm{\$5,231.18}$

2. Break-even point (months): 48.2

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$225,000.00}$$=\mathrm{\$4,500.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{6.5\%}-2\times \mathrm{0.32\%}$$=\mathrm{5.86\%}$

3. Monthly payment at 6.5% over 360 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$225,000.00}\times \frac{0.00541667}{\left(1-{\left(1+0.00541667\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$1,422.15}$

4. Monthly payment at 5.86%

   $\mathrm{\$225,000.00}\times \frac{0.00488333}{\left(1-{\left(1+0.00488333\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$1,328.80}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$1,422.15}-\mathrm{\$1,328.80}$$=\mathrm{\$93.35}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$4,500.00}}{\mathrm{\$93.35}}$$=48.206$

7. Net benefit after 96 months: payment savings, plus the lower balance still owed ($196,910.53 instead of $199,477.52), minus the points cost

   $96\times \mathrm{\$93.35}+\mathrm{\$2,566.99}-\mathrm{\$4,500.00}$$=\mathrm{\$7,028.53}$

3. Break-even point (months): 54.4

1. Cost of the points: each point is 1% of the loan

   $\frac{3}{100}\times \mathrm{\$300,000.00}$$=\mathrm{\$9,000.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{5.5\%}-3\times \mathrm{0.3\%}$$=\mathrm{4.6\%}$

3. Monthly payment at 5.5% over 360 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$300,000.00}\times \frac{0.00458333}{\left(1-{\left(1+0.00458333\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$1,703.37}$

4. Monthly payment at 4.6%

   $\mathrm{\$300,000.00}\times \frac{0.00383333}{\left(1-{\left(1+0.00383333\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$1,537.93}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$1,703.37}-\mathrm{\$1,537.93}$$=\mathrm{\$165.43}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$9,000.00}}{\mathrm{\$165.43}}$$=54.4024$

7. Net benefit after 180 months: payment savings, plus the lower balance still owed ($199,702.02 instead of $208,469.16), minus the points cost

   $180\times \mathrm{\$165.43}+\mathrm{\$8,767.13}-\mathrm{\$9,000.00}$$=\mathrm{\$29,545.24}$

4. Break-even point (months): 95.3

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$275,000.00}$$=\mathrm{\$5,500.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{8.5\%}-2\times \mathrm{0.18\%}$$=\mathrm{8.14\%}$

3. Monthly payment at 8.5% over 180 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$275,000.00}\times \frac{0.00708333}{\left(1-{\left(1+0.00708333\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$2,708.03}$

4. Monthly payment at 8.14%

   $\mathrm{\$275,000.00}\times \frac{0.00678333}{\left(1-{\left(1+0.00678333\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$2,650.32}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,708.03}-\mathrm{\$2,650.32}$$=\mathrm{\$57.72}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$5,500.00}}{\mathrm{\$57.72}}$$=95.2936$

7. Net benefit after 132 months: payment savings, plus the lower balance still owed ($108,270.39 instead of $109,866.94), minus the points cost

   $132\times \mathrm{\$57.72}+\mathrm{\$1,596.56}-\mathrm{\$5,500.00}$$=\mathrm{\$3,715.12}$

5. Break-even point (months): 105.6

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$350,000.00}$$=\mathrm{\$7,000.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{6.8\%}-2\times \mathrm{0.16\%}$$=\mathrm{6.48\%}$

3. Monthly payment at 6.8% over 240 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$350,000.00}\times \frac{0.00566667}{\left(1-{\left(1+0.00566667\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,671.69}$

4. Monthly payment at 6.48%

   $\mathrm{\$350,000.00}\times \frac{0.0054}{\left(1-{\left(1+0.0054\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,605.39}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,671.69}-\mathrm{\$2,605.39}$$=\mathrm{\$66.30}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$7,000.00}}{\mathrm{\$66.30}}$$=105.5777$

7. Net benefit after 108 months: payment savings, plus the lower balance still owed ($245,480.20 instead of $247,848.15), minus the points cost

   $108\times \mathrm{\$66.30}+\mathrm{\$2,367.95}-\mathrm{\$7,000.00}$$=\mathrm{\$2,528.55}$

6. Break-even point (months): 72.6

1. Cost of the points: each point is 1% of the loan

   $\frac{3}{100}\times \mathrm{\$375,000.00}$$=\mathrm{\$11,250.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{5.8\%}-3\times \mathrm{0.22\%}$$=\mathrm{5.14\%}$

3. Monthly payment at 5.8% over 360 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$375,000.00}\times \frac{0.00483333}{\left(1-{\left(1+0.00483333\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$2,200.32}$

4. Monthly payment at 5.14%

   $\mathrm{\$375,000.00}\times \frac{0.00428333}{\left(1-{\left(1+0.00428333\right)}^{\mathrm{-360}}\right)}$$=\mathrm{\$2,045.29}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,200.32}-\mathrm{\$2,045.29}$$=\mathrm{\$155.04}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$11,250.00}}{\mathrm{\$155.04}}$$=72.5641$

7. Net benefit after 84 months: payment savings, plus the lower balance still owed ($330,726.25 instead of $334,933.61), minus the points cost

   $84\times \mathrm{\$155.04}+\mathrm{\$4,207.36}-\mathrm{\$11,250.00}$$=\mathrm{\$5,980.33}$

7. Break-even point (months): 53

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$320,000.00}$$=\mathrm{\$6,400.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{9\%}-2\times \mathrm{0.32\%}$$=\mathrm{8.36\%}$

3. Monthly payment at 9% over 180 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$320,000.00}\times \frac{0.0075}{\left(1-{\left(1+0.0075\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$3,245.65}$

4. Monthly payment at 8.36%

   $\mathrm{\$320,000.00}\times \frac{0.00696667}{\left(1-{\left(1+0.00696667\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$3,124.96}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$3,245.65}-\mathrm{\$3,124.96}$$=\mathrm{\$120.69}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$6,400.00}}{\mathrm{\$120.69}}$$=53.0276$

7. Net benefit after 96 months: payment savings, plus the lower balance still owed ($198,206.68 instead of $201,730.21), minus the points cost

   $96\times \mathrm{\$120.69}+\mathrm{\$3,523.52}-\mathrm{\$6,400.00}$$=\mathrm{\$8,709.93}$

8. Break-even point (months): 74.9

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$280,000.00}$$=\mathrm{\$5,600.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{7.5\%}-2\times \mathrm{0.22\%}$$=\mathrm{7.06\%}$

3. Monthly payment at 7.5% over 240 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$280,000.00}\times \frac{0.00625}{\left(1-{\left(1+0.00625\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,255.66}$

4. Monthly payment at 7.06%

   $\mathrm{\$280,000.00}\times \frac{0.00588333}{\left(1-{\left(1+0.00588333\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$2,180.93}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,255.66}-\mathrm{\$2,180.93}$$=\mathrm{\$74.73}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$5,600.00}}{\mathrm{\$74.73}}$$=74.9382$

7. Net benefit after 96 months: payment savings, plus the lower balance still owed ($211,416.27 instead of $213,760.87), minus the points cost

   $96\times \mathrm{\$74.73}+\mathrm{\$2,344.60}-\mathrm{\$5,600.00}$$=\mathrm{\$3,918.51}$

9. Break-even point (months): 83.3

1. Cost of the points: each point is 1% of the loan

   $\frac{2}{100}\times \mathrm{\$275,000.00}$$=\mathrm{\$5,500.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{6.5\%}-2\times \mathrm{0.22\%}$$=\mathrm{6.06\%}$

3. Monthly payment at 6.5% over 180 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$275,000.00}\times \frac{0.00541667}{\left(1-{\left(1+0.00541667\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$2,395.55}$

4. Monthly payment at 6.06%

   $\mathrm{\$275,000.00}\times \frac{0.00505}{\left(1-{\left(1+0.00505\right)}^{\mathrm{-180}}\right)}$$=\mathrm{\$2,329.53}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$2,395.55}-\mathrm{\$2,329.53}$$=\mathrm{\$66.02}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$5,500.00}}{\mathrm{\$66.02}}$$=83.3141$

7. Net benefit after 120 months: payment savings, plus the lower balance still owed ($120,322.53 instead of $122,433.15), minus the points cost

   $120\times \mathrm{\$66.02}+\mathrm{\$2,110.62}-\mathrm{\$5,500.00}$$=\mathrm{\$4,532.45}$

10. Break-even point (months): 77.9

1. Cost of the points: each point is 1% of the loan

   $\frac{3}{100}\times \mathrm{\$240,000.00}$$=\mathrm{\$7,200.00}$

2. Find your new rate: take the rate without points and subtract what the points knock off

   $\mathrm{6.6\%}-3\times \mathrm{0.22\%}$$=\mathrm{5.94\%}$

3. Monthly payment at 6.6% over 240 months. P is the loan, i is the yearly rate ÷ 12 and n is the number of payments

   $\mathrm{\$240,000.00}\times \frac{0.0055}{\left(1-{\left(1+0.0055\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$1,803.53}$

4. Monthly payment at 5.94%

   $\mathrm{\$240,000.00}\times \frac{0.00495}{\left(1-{\left(1+0.00495\right)}^{\mathrm{-240}}\right)}$$=\mathrm{\$1,711.14}$

5. Subtract the two payments to see what the lower rate saves you each month

   $\mathrm{\$1,803.53}-\mathrm{\$1,711.14}$$=\mathrm{\$92.40}$

6. Break-even: divide the cost by the monthly saving to see how many months it takes to earn the points back

   $\frac{\mathrm{\$7,200.00}}{\mathrm{\$92.40}}$$=77.9258$

7. Net benefit after 108 months: payment savings, plus the lower balance still owed ($165,543.69 instead of $168,940.57), minus the points cost

   $108\times \mathrm{\$92.40}+\mathrm{\$3,396.88}-\mathrm{\$7,200.00}$$=\mathrm{\$6,175.60}$