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Cash-Out 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.
- Home value: $425,000
- Current mortgage balance: $200,000
- Current interest rate: 3.25%
- Time left on current loan: 24 years
- Lender's loan-to-value limit: 85%
- Cash you want: $52,500
- New interest rate: 4.6%
- New loan term: 15 years
- Closing costs: $7,750
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 8.5%
- Second loan term: 20 years
Find: Cash available
Answer
2.
Problem 2.
- Home value: $475,000
- Current mortgage balance: $250,000
- Current interest rate: 3%
- Time left on current loan: 24 years
- Lender's loan-to-value limit: 85%
- Cash you want: $68,000
- New interest rate: 6.75%
- New loan term: 30 years
- Closing costs: $7,500
- How closing costs are paid: Added to the new loan
- Second loan rate to compare: 6%
- Second loan term: 10 years
Find: Cash available
Answer
3.
Problem 3.
- Home value: $420,000
- Current mortgage balance: $225,000
- Current interest rate: 4.5%
- Time left on current loan: 28 years
- Lender's loan-to-value limit: 85%
- Cash you want: $60,000
- New interest rate: 5.9%
- New loan term: 20 years
- Closing costs: $10,000
- How closing costs are paid: Added to the new loan
- Second loan rate to compare: 7.5%
- Second loan term: 10 years
Find: Cash available
Answer
4.
Problem 4.
- Home value: $500,000
- Current mortgage balance: $250,000
- Current interest rate: 4.5%
- Time left on current loan: 22 years
- Lender's loan-to-value limit: 75%
- Cash you want: $75,000
- New interest rate: 7%
- New loan term: 15 years
- Closing costs: $8,250
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 7.2%
- Second loan term: 10 years
Find: Cash available
Answer
5.
Problem 5.
- Home value: $500,000
- Current mortgage balance: $250,000
- Current interest rate: 3%
- Time left on current loan: 34 years
- Lender's loan-to-value limit: 70%
- Cash you want: $70,000
- New interest rate: 6.25%
- New loan term: 15 years
- Closing costs: $6,500
- How closing costs are paid: Added to the new loan
- Second loan rate to compare: 10%
- Second loan term: 10 years
Find: Cash available
Answer
6.
Problem 6.
- Home value: $500,000
- Current mortgage balance: $220,000
- Current interest rate: 2.8%
- Time left on current loan: 22 years
- Lender's loan-to-value limit: 75%
- Cash you want: $55,000
- New interest rate: 5%
- New loan term: 20 years
- Closing costs: $5,800
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 9.5%
- Second loan term: 15 years
Find: Cash available
Answer
7.
Problem 7.
- Home value: $500,000
- Current mortgage balance: $280,000
- Current interest rate: 4%
- Time left on current loan: 26 years
- Lender's loan-to-value limit: 70%
- Cash you want: $55,000
- New interest rate: 6.5%
- New loan term: 30 years
- Closing costs: $9,500
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 7.25%
- Second loan term: 15 years
Find: Cash available
Answer
8.
Problem 8.
- Home value: $600,000
- Current mortgage balance: $190,000
- Current interest rate: 2.4%
- Time left on current loan: 22 years
- Lender's loan-to-value limit: 80%
- Cash you want: $80,000
- New interest rate: 7.4%
- New loan term: 20 years
- Closing costs: $7,500
- How closing costs are paid: Added to the new loan
- Second loan rate to compare: 10%
- Second loan term: 20 years
Find: Cash available
Answer
9.
Problem 9.
- Home value: $375,000
- Current mortgage balance: $200,000
- Current interest rate: 3.5%
- Time left on current loan: 20 years
- Lender's loan-to-value limit: 80%
- Cash you want: $52,500
- New interest rate: 6.5%
- New loan term: 30 years
- Closing costs: $8,000
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 7.4%
- Second loan term: 20 years
Find: Cash available
Answer
10.
Problem 10.
- Home value: $500,000
- Current mortgage balance: $200,000
- Current interest rate: 2.7%
- Time left on current loan: 22 years
- Lender's loan-to-value limit: 75%
- Cash you want: $45,000
- New interest rate: 7%
- New loan term: 15 years
- Closing costs: $8,000
- How closing costs are paid: Paid in cash
- Second loan rate to compare: 4.75%
- Second loan term: 20 years
Find: Cash available
Answer

Answer key: Cash-Out Refinance worksheet

1. Cash available: $161,250.00
1. Find the most a lender would let you owe: 85% of the home's value
  $$425,000.00 \times 85%$ $= $361,250.00$
2. Subtract what you owe now. What's left is the cash available
  $$361,250.00 - $200,000.00$ $= $161,250.00$
3. Find the new loan: your balance plus the cash you take
  $$200,000.00 + $52,500.00$ $= $252,500.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 288 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$200,000.00 \times 0.00270833}{1 - {(1 + 0.00270833)}^{−288}}$ $= $1,001.03$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$252,500.00 \times 0.00383333}{1 - {(1 + 0.00383333)}^{−180}}$ $= $1,944.54$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$1,944.54 \times 180 + $7,750.00 - $1,001.03 \times 288 - $52,500.00$ $= $16,970.72$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$52,500.00 \times 0.00708333}{1 - {(1 + 0.00708333)}^{−240}}$ $= $455.61$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$455.61 \times 240 - $52,500.00$ $= $56,845.73$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$252,500.00}{$425,000.00}$ $= 59.41%$
2. Cash available: $146,250.00
1. Find the most a lender would let you owe: 85% of the home's value
  $$475,000.00 \times 85%$ $= $403,750.00$
2. Subtract what you owe now and the closing costs. What's left is the cash available
  $$403,750.00 - $250,000.00 - $7,500.00$ $= $146,250.00$
3. Find the new loan: your balance, the cash you take, and the closing costs
  $$250,000.00 + $68,000.00 + $7,500.00$ $= $325,500.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 288 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$250,000.00 \times 0.0025}{1 - {(1 + 0.0025)}^{−288}}$ $= $1,218.77$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 360 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$325,500.00 \times 0.005625}{1 - {(1 + 0.005625)}^{−360}}$ $= $2,111.19$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,111.19 \times 360 + $0.00 - $1,218.77 \times 288 - $68,000.00$ $= $341,020.19$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 120 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$68,000.00 \times 0.005}{1 - {(1 + 0.005)}^{−120}}$ $= $754.94$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$754.94 \times 120 - $68,000.00$ $= $22,592.73$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$325,500.00}{$475,000.00}$ $= 68.53%$
3. Cash available: $122,000.00
1. Find the most a lender would let you owe: 85% of the home's value
  $$420,000.00 \times 85%$ $= $357,000.00$
2. Subtract what you owe now and the closing costs. What's left is the cash available
  $$357,000.00 - $225,000.00 - $10,000.00$ $= $122,000.00$
3. Find the new loan: your balance, the cash you take, and the closing costs
  $$225,000.00 + $60,000.00 + $10,000.00$ $= $295,000.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 336 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$225,000.00 \times 0.00375}{1 - {(1 + 0.00375)}^{−336}}$ $= $1,178.95$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$295,000.00 \times 0.00491667}{1 - {(1 + 0.00491667)}^{−240}}$ $= $2,096.49$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,096.49 \times 240 + $0.00 - $1,178.95 \times 336 - $60,000.00$ $= $47,028.61$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 120 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$60,000.00 \times 0.00625}{1 - {(1 + 0.00625)}^{−120}}$ $= $712.21$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$712.21 \times 120 - $60,000.00$ $= $25,465.27$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$295,000.00}{$420,000.00}$ $= 70.24%$
4. Cash available: $125,000.00
1. Find the most a lender would let you owe: 75% of the home's value
  $$500,000.00 \times 75%$ $= $375,000.00$
2. Subtract what you owe now. What's left is the cash available
  $$375,000.00 - $250,000.00$ $= $125,000.00$
3. Find the new loan: your balance plus the cash you take
  $$250,000.00 + $75,000.00$ $= $325,000.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 264 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$250,000.00 \times 0.00375}{1 - {(1 + 0.00375)}^{−264}}$ $= $1,493.47$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$325,000.00 \times 0.00583333}{1 - {(1 + 0.00583333)}^{−180}}$ $= $2,921.19$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,921.19 \times 180 + $8,250.00 - $1,493.47 \times 264 - $75,000.00$ $= $64,789.67$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 120 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$75,000.00 \times 0.006}{1 - {(1 + 0.006)}^{−120}}$ $= $878.56$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$878.56 \times 120 - $75,000.00$ $= $30,427.69$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$325,000.00}{$500,000.00}$ $= 65%$
5. Cash available: $93,500.00
1. Find the most a lender would let you owe: 70% of the home's value
  $$500,000.00 \times 70%$ $= $350,000.00$
2. Subtract what you owe now and the closing costs. What's left is the cash available
  $$350,000.00 - $250,000.00 - $6,500.00$ $= $93,500.00$
3. Find the new loan: your balance, the cash you take, and the closing costs
  $$250,000.00 + $70,000.00 + $6,500.00$ $= $326,500.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 408 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$250,000.00 \times 0.0025}{1 - {(1 + 0.0025)}^{−408}}$ $= $978.17$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$326,500.00 \times 0.00520833}{1 - {(1 + 0.00520833)}^{−180}}$ $= $2,799.49$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,799.49 \times 180 + $0.00 - $978.17 \times 408 - $70,000.00$ $= $34,812.52$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 120 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$70,000.00 \times 0.00833333}{1 - {(1 + 0.00833333)}^{−120}}$ $= $925.06$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$925.06 \times 120 - $70,000.00$ $= $41,006.62$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$326,500.00}{$500,000.00}$ $= 65.3%$
6. Cash available: $155,000.00
1. Find the most a lender would let you owe: 75% of the home's value
  $$500,000.00 \times 75%$ $= $375,000.00$
2. Subtract what you owe now. What's left is the cash available
  $$375,000.00 - $220,000.00$ $= $155,000.00$
3. Find the new loan: your balance plus the cash you take
  $$220,000.00 + $55,000.00$ $= $275,000.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 264 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$220,000.00 \times 0.00233333}{1 - {(1 + 0.00233333)}^{−264}}$ $= $1,117.13$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$275,000.00 \times 0.00416667}{1 - {(1 + 0.00416667)}^{−240}}$ $= $1,814.88$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$1,814.88 \times 240 + $5,800.00 - $1,117.13 \times 264 - $55,000.00$ $= $91,449.08$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$55,000.00 \times 0.00791667}{1 - {(1 + 0.00791667)}^{−180}}$ $= $574.32$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$574.32 \times 180 - $55,000.00$ $= $48,378.24$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$275,000.00}{$500,000.00}$ $= 55%$
7. Cash available: $70,000.00
1. Find the most a lender would let you owe: 70% of the home's value
  $$500,000.00 \times 70%$ $= $350,000.00$
2. Subtract what you owe now. What's left is the cash available
  $$350,000.00 - $280,000.00$ $= $70,000.00$
3. Find the new loan: your balance plus the cash you take
  $$280,000.00 + $55,000.00$ $= $335,000.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 312 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$280,000.00 \times 0.00333333}{1 - {(1 + 0.00333333)}^{−312}}$ $= $1,444.94$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 360 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$335,000.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−360}}$ $= $2,117.43$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,117.43 \times 360 + $9,500.00 - $1,444.94 \times 312 - $55,000.00$ $= $265,953.63$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$55,000.00 \times 0.00604167}{1 - {(1 + 0.00604167)}^{−180}}$ $= $502.07$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$502.07 \times 180 - $55,000.00$ $= $35,373.43$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$335,000.00}{$500,000.00}$ $= 67%$
8. Cash available: $282,500.00
1. Find the most a lender would let you owe: 80% of the home's value
  $$600,000.00 \times 80%$ $= $480,000.00$
2. Subtract what you owe now and the closing costs. What's left is the cash available
  $$480,000.00 - $190,000.00 - $7,500.00$ $= $282,500.00$
3. Find the new loan: your balance, the cash you take, and the closing costs
  $$190,000.00 + $80,000.00 + $7,500.00$ $= $277,500.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 264 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$190,000.00 \times 0.002}{1 - {(1 + 0.002)}^{−264}}$ $= $927.04$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$277,500.00 \times 0.00616667}{1 - {(1 + 0.00616667)}^{−240}}$ $= $2,218.58$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,218.58 \times 240 + $0.00 - $927.04 \times 264 - $80,000.00$ $= $207,720.79$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$80,000.00 \times 0.00833333}{1 - {(1 + 0.00833333)}^{−240}}$ $= $772.02$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$772.02 \times 240 - $80,000.00$ $= $105,284.16$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$277,500.00}{$600,000.00}$ $= 46.25%$
9. Cash available: $100,000.00
1. Find the most a lender would let you owe: 80% of the home's value
  $$375,000.00 \times 80%$ $= $300,000.00$
2. Subtract what you owe now. What's left is the cash available
  $$300,000.00 - $200,000.00$ $= $100,000.00$
3. Find the new loan: your balance plus the cash you take
  $$200,000.00 + $52,500.00$ $= $252,500.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$200,000.00 \times 0.00291667}{1 - {(1 + 0.00291667)}^{−240}}$ $= $1,159.92$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 360 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$252,500.00 \times 0.00541667}{1 - {(1 + 0.00541667)}^{−360}}$ $= $1,595.97$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$1,595.97 \times 360 + $8,000.00 - $1,159.92 \times 240 - $52,500.00$ $= $251,669.17$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$52,500.00 \times 0.00616667}{1 - {(1 + 0.00616667)}^{−240}}$ $= $419.73$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$419.73 \times 240 - $52,500.00$ $= $48,235.69$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$252,500.00}{$375,000.00}$ $= 67.33%$
10. Cash available: $175,000.00
1. Find the most a lender would let you owe: 75% of the home's value
  $$500,000.00 \times 75%$ $= $375,000.00$
2. Subtract what you owe now. What's left is the cash available
  $$375,000.00 - $200,000.00$ $= $175,000.00$
3. Find the new loan: your balance plus the cash you take
  $$200,000.00 + $45,000.00$ $= $245,000.00$
4. Find your current payment. A standard formula finds the one amount that clears the loan in 264 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$200,000.00 \times 0.00225}{1 - {(1 + 0.00225)}^{−264}}$ $= $1,005.55$
5. Find the new payment. Remember, it replaces your whole mortgage, not only the cash. A standard formula finds the one amount that clears the loan in 180 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$245,000.00 \times 0.00583333}{1 - {(1 + 0.00583333)}^{−180}}$ $= $2,202.13$
6. See what taking the cash costs on this plan: all its payments and cash costs, minus the rest of your current loan, minus the cash
  $$2,202.13 \times 180 + $8,000.00 - $1,005.55 \times 264 - $45,000.00$ $= $93,918.54$
7. Find the payment on a second loan for the same cash, keeping your current mortgage. A standard formula finds the one amount that clears the loan in 240 months, where the monthly rate is the yearly rate ÷ 12
  $\frac{$45,000.00 \times 0.00395833}{1 - {(1 + 0.00395833)}^{−240}}$ $= $290.80$
8. See what the cash costs on that plan: the second loan's payments minus the cash
  $$290.80 \times 240 - $45,000.00$ $= $24,792.15$
9. Check how much you'd owe against the home after the cash-out
  $\frac{$245,000.00}{$500,000.00}$ $= 49%$