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Refinance worksheet

Grades 11–12 · CCSS HSA.SSE.B.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Current loan balance: $275,000
- Current interest rate: 7.5%
- Time left on current loan: 32 years
- New interest rate: 5%
- New loan term: 28 years
- Closing costs: $3,500
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer
2.
Problem 2.
- Current loan balance: $240,000
- Current interest rate: 7.75%
- Time left on current loan: 32 years
- New interest rate: 5%
- New loan term: 30 years
- Closing costs: $4,000
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer
3.
Problem 3.
- Current loan balance: $340,000
- Current interest rate: 10%
- Time left on current loan: 40 years
- New interest rate: 5%
- New loan term: 38 years
- Closing costs: $5,500
- How closing costs are paid: Paid in cash
Find: Monthly savings
Answer
4.
Problem 4.
- Current loan balance: $220,000
- Current interest rate: 7.8%
- Time left on current loan: 32 years
- New interest rate: 6%
- New loan term: 30 years
- Closing costs: $3,250
- How closing costs are paid: Paid in cash
Find: Monthly savings
Answer
5.
Problem 5.
- Current loan balance: $250,000
- Current interest rate: 9%
- Time left on current loan: 23 years
- New interest rate: 7%
- New loan term: 28 years
- Closing costs: $4,400
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer
6.
Problem 6.
- Current loan balance: $300,000
- Current interest rate: 10%
- Time left on current loan: 22 years
- New interest rate: 8%
- New loan term: 20 years
- Closing costs: $3,750
- How closing costs are paid: Paid in cash
Find: Monthly savings
Answer
7.
Problem 7.
- Current loan balance: $325,000
- Current interest rate: 6.5%
- Time left on current loan: 22 years
- New interest rate: 5%
- New loan term: 34 years
- Closing costs: $5,000
- How closing costs are paid: Paid in cash
Find: Monthly savings
Answer
8.
Problem 8.
- Current loan balance: $225,000
- Current interest rate: 6.5%
- Time left on current loan: 30 years
- New interest rate: 5%
- New loan term: 32 years
- Closing costs: $6,100
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer
9.
Problem 9.
- Current loan balance: $240,000
- Current interest rate: 6.5%
- Time left on current loan: 34 years
- New interest rate: 5%
- New loan term: 28 years
- Closing costs: $4,500
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer
10.
Problem 10.
- Current loan balance: $365,000
- Current interest rate: 8%
- Time left on current loan: 27 years
- New interest rate: 5%
- New loan term: 32 years
- Closing costs: $4,750
- How closing costs are paid: Added to the new loan
Find: Monthly savings
Answer

Answer key: Refinance worksheet

1. Monthly savings: $349.94
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$275,000.00 at 7.5% over 384 months$ $= $1,891.64$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$275,000.00 + $3,500.00$ $= $278,500.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$278,500.00 at 5% over 336 months$ $= $1,541.70$
4. Subtract the new payment from the current one to see what you save each month
  $$1,891.64 - $1,541.70$ $= $349.94$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($1,891.64 \times 384 - $275,000.00) - ($1,541.70 \times 336 - $278,500.00)$ $= $211,878.33$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$3,500.00}{$349.94}$ $= 11 months$
2. Monthly savings: $383.06
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$240,000.00 at 7.75% over 384 months$ $= $1,692.90$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$240,000.00 + $4,000.00$ $= $244,000.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$244,000.00 at 5% over 360 months$ $= $1,309.84$
4. Subtract the new payment from the current one to see what you save each month
  $$1,692.90 - $1,309.84$ $= $383.06$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($1,692.90 \times 384 - $240,000.00) - ($1,309.84 \times 360 - $244,000.00)$ $= $182,531.12$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$4,000.00}{$383.06}$ $= 11 months$
3. Monthly savings: $1,220.12
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$340,000.00 at 10% over 480 months$ $= $2,887.10$
2. Find the new monthly payment the same way, using the new amount, rate and term
  $$340,000.00 at 5% over 456 months$ $= $1,666.98$
3. Subtract the new payment from the current one to see what you save each month
  $$2,887.10 - $1,666.98$ $= $1,220.12$
4. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($2,887.10 \times 480 - $340,000.00) - ($1,666.98 \times 456 - $340,000.00)$ $= $625,662.87$
5. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$5,500.00}{$1,220.12}$ $= 5 months$
4. Monthly savings: $240.56
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$220,000.00 at 7.8% over 384 months$ $= $1,559.57$
2. Find the new monthly payment the same way, using the new amount, rate and term
  $$220,000.00 at 6% over 360 months$ $= $1,319.01$
3. Subtract the new payment from the current one to see what you save each month
  $$1,559.57 - $1,319.01$ $= $240.56$
4. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($1,559.57 \times 384 - $220,000.00) - ($1,319.01 \times 360 - $220,000.00)$ $= $124,032.01$
5. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$3,250.00}{$240.56}$ $= 14 months$
5. Monthly savings: $419.25
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$250,000.00 at 9% over 276 months$ $= $2,148.17$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$250,000.00 + $4,400.00$ $= $254,400.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$254,400.00 at 7% over 336 months$ $= $1,728.92$
4. Subtract the new payment from the current one to see what you save each month
  $$2,148.17 - $1,728.92$ $= $419.25$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($2,148.17 \times 276 - $250,000.00) - ($1,728.92 \times 336 - $254,400.00)$ $= $16,376.45$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$4,400.00}{$419.25}$ $= 11 months$
6. Monthly savings: $305.42
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$300,000.00 at 10% over 264 months$ $= $2,814.74$
2. Find the new monthly payment the same way, using the new amount, rate and term
  $$300,000.00 at 8% over 240 months$ $= $2,509.32$
3. Subtract the new payment from the current one to see what you save each month
  $$2,814.74 - $2,509.32$ $= $305.42$
4. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($2,814.74 \times 264 - $300,000.00) - ($2,509.32 \times 240 - $300,000.00)$ $= $140,853.98$
5. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$3,750.00}{$305.42}$ $= 13 months$
7. Monthly savings: $658.90
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$325,000.00 at 6.5% over 264 months$ $= $2,317.05$
2. Find the new monthly payment the same way, using the new amount, rate and term
  $$325,000.00 at 5% over 408 months$ $= $1,658.16$
3. Subtract the new payment from the current one to see what you save each month
  $$2,317.05 - $1,658.16$ $= $658.90$
4. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($2,317.05 \times 264 - $325,000.00) - ($1,658.16 \times 408 - $325,000.00)$ $= −$64,826.09$
5. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$5,000.00}{$658.90}$ $= 8 months$
8. Monthly savings: $214.63
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$225,000.00 at 6.5% over 360 months$ $= $1,422.15$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$225,000.00 + $6,100.00$ $= $231,100.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$231,100.00 at 5% over 384 months$ $= $1,207.52$
4. Subtract the new payment from the current one to see what you save each month
  $$1,422.15 - $1,207.52$ $= $214.63$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($1,422.15 \times 360 - $225,000.00) - ($1,207.52 \times 384 - $231,100.00)$ $= $54,386.22$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$6,100.00}{$214.63}$ $= 29 months$
9. Monthly savings: $107.77
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$240,000.00 at 6.5% over 408 months$ $= $1,461.26$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$240,000.00 + $4,500.00$ $= $244,500.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$244,500.00 at 5% over 336 months$ $= $1,353.49$
4. Subtract the new payment from the current one to see what you save each month
  $$1,461.26 - $1,353.49$ $= $107.77$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($1,461.26 \times 408 - $240,000.00) - ($1,353.49 \times 336 - $244,500.00)$ $= $145,922.03$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$4,500.00}{$107.77}$ $= 42 months$
10. Monthly savings: $821.14
1. Find your current monthly payment: the same amount each month that pays off what you owe in the time left
  $$365,000.00 at 8% over 324 months$ $= $2,753.12$
2. Add the closing costs to what you borrow, since you chose to put them into the new loan
  $$365,000.00 + $4,750.00$ $= $369,750.00$
3. Find the new monthly payment the same way, using the new amount, rate and term
  $$369,750.00 at 5% over 384 months$ $= $1,931.98$
4. Subtract the new payment from the current one to see what you save each month
  $$2,753.12 - $1,931.98$ $= $821.14$
5. Compare total interest: what is left to pay on the current loan minus what the new loan will cost
  $($2,753.12 \times 324 - $365,000.00) - ($1,931.98 \times 384 - $369,750.00)$ $= $154,879.22$
6. Find the break-even month: divide the closing costs by your monthly savings to see how long they take to pay back, then round up
  $\frac{$4,750.00}{$821.14}$ $= 6 months$