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Home Affordability 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.
    • Gross annual income: $100,000
    • Other monthly debt payments: $700
    • Down payment: $70,000
    • Mortgage interest rate: 5%
    • Loan term: 20 years
    • Property tax rate: 1% of price per year
    • Home insurance: $1,300 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 26% of gross income
    • Total debt limit (back-end ratio): 36% of gross income

    Find: Maximum home price

  2. Problem 2.
    • Gross annual income: $142,500
    • Other monthly debt payments: $550
    • Down payment: $55,000
    • Mortgage interest rate: 4%
    • Loan term: 30 years
    • Property tax rate: 1.3% of price per year
    • Home insurance: $2,000 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 38% of gross income
    • Total debt limit (back-end ratio): 30% of gross income

    Find: Maximum home price

  3. Problem 3.
    • Gross annual income: $150,000
    • Other monthly debt payments: $680
    • Down payment: $60,000
    • Mortgage interest rate: 6%
    • Loan term: 20 years
    • Property tax rate: 1.2% of price per year
    • Home insurance: $1,700 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 26% of gross income
    • Total debt limit (back-end ratio): 22% of gross income

    Find: Maximum home price

  4. Problem 4.
    • Gross annual income: $110,000
    • Other monthly debt payments: $600
    • Down payment: $92,000
    • Mortgage interest rate: 5.8%
    • Loan term: 30 years
    • Property tax rate: 1% of price per year
    • Home insurance: $2,000 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 24% of gross income
    • Total debt limit (back-end ratio): 45% of gross income

    Find: Maximum home price

  5. Problem 5.
    • Gross annual income: $110,000
    • Other monthly debt payments: $450
    • Down payment: $60,000
    • Mortgage interest rate: 5.8%
    • Loan term: 15 years
    • Property tax rate: 1.3% of price per year
    • Home insurance: $1,800 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 35% of gross income
    • Total debt limit (back-end ratio): 36% of gross income

    Find: Maximum home price

  6. Problem 6.
    • Gross annual income: $120,000
    • Other monthly debt payments: $560
    • Down payment: $75,000
    • Mortgage interest rate: 5.4%
    • Loan term: 30 years
    • Property tax rate: 1% of price per year
    • Home insurance: $1,575 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 26% of gross income
    • Total debt limit (back-end ratio): 32% of gross income

    Find: Maximum home price

  7. Problem 7.
    • Gross annual income: $125,000
    • Other monthly debt payments: $600
    • Down payment: $55,000
    • Mortgage interest rate: 5.8%
    • Loan term: 20 years
    • Property tax rate: 0.9% of price per year
    • Home insurance: $950 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 36% of gross income
    • Total debt limit (back-end ratio): 38% of gross income

    Find: Maximum home price

  8. Problem 8.
    • Gross annual income: $120,000
    • Other monthly debt payments: $500
    • Down payment: $52,500
    • Mortgage interest rate: 8%
    • Loan term: 30 years
    • Property tax rate: 1% of price per year
    • Home insurance: $2,000 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 28% of gross income
    • Total debt limit (back-end ratio): 45% of gross income

    Find: Maximum home price

  9. Problem 9.
    • Gross annual income: $110,000
    • Other monthly debt payments: $660
    • Down payment: $56,000
    • Mortgage interest rate: 6%
    • Loan term: 15 years
    • Property tax rate: 1.4% of price per year
    • Home insurance: $1,800 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 30% of gross income
    • Total debt limit (back-end ratio): 38% of gross income

    Find: Maximum home price

  10. Problem 10.
    • Gross annual income: $130,000
    • Other monthly debt payments: $500
    • Down payment: $70,000
    • Mortgage interest rate: 6%
    • Loan term: 30 years
    • Property tax rate: 0.9% of price per year
    • Home insurance: $1,675 per year
    • HOA dues: $0 per month
    • PMI rate: 0% of loan per year
    • Housing cost limit (front-end ratio): 20% of gross income
    • Total debt limit (back-end ratio): 35% of gross income

    Find: Maximum home price

Answer key: Home Affordability worksheet

  1. 1. Maximum home price: $339,074.32

    1. Find your monthly income before tax: yearly income ÷ 12

      $100,000.0012=$8,333.33
    2. Housing limit: up to 26% of your monthly income can go to housing

      $8,333.33×26%=$2,166.67
    3. Total debt limit: 36% of your monthly income, minus what your other debts already take

      $8,333.33×36%−$700.00=$2,300.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,166.67
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00659956+0%12=0.00659956
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1%12=0.00083333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,166.67−$108.33+0.00659956×$70,000.00(0.00659956+0.00083333)=$339,074.32
  2. 2. Maximum home price: $530,673.33

    1. Find your monthly income before tax: yearly income ÷ 12

      $142,500.0012=$11,875.00
    2. Housing limit: up to 38% of your monthly income can go to housing

      $11,875.00×38%=$4,512.50
    3. Total debt limit: 30% of your monthly income, minus what your other debts already take

      $11,875.00×30%−$550.00=$3,012.50
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the total debt limit)

      H=$3,012.50
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00477415+0%12=0.00477415
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1.3%12=0.00108333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$3,012.50−$166.67+0.00477415×$55,000.00(0.00477415+0.00108333)=$530,673.33
  3. 3. Maximum home price: $288,841.53

    1. Find your monthly income before tax: yearly income ÷ 12

      $150,000.0012=$12,500.00
    2. Housing limit: up to 26% of your monthly income can go to housing

      $12,500.00×26%=$3,250.00
    3. Total debt limit: 22% of your monthly income, minus what your other debts already take

      $12,500.00×22%−$680.00=$2,070.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the total debt limit)

      H=$2,070.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00716431+0%12=0.00716431
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1.2%12=0.001
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,070.00−$141.67+0.00716431×$60,000.00(0.00716431+0.001)=$288,841.53
  4. 4. Maximum home price: $384,002.16

    1. Find your monthly income before tax: yearly income ÷ 12

      $110,000.0012=$9,166.67
    2. Housing limit: up to 24% of your monthly income can go to housing

      $9,166.67×24%=$2,200.00
    3. Total debt limit: 45% of your monthly income, minus what your other debts already take

      $9,166.67×45%−$600.00=$3,525.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,200.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00586753+0%12=0.00586753
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1%12=0.00083333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,200.00−$166.67+0.00586753×$92,000.00(0.00586753+0.00083333)=$384,002.16
  5. 5. Maximum home price: $339,895.38

    1. Find your monthly income before tax: yearly income ÷ 12

      $110,000.0012=$9,166.67
    2. Housing limit: up to 35% of your monthly income can go to housing

      $9,166.67×35%=$3,208.33
    3. Total debt limit: 36% of your monthly income, minus what your other debts already take

      $9,166.67×36%−$450.00=$2,850.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the total debt limit)

      H=$2,850.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.0083309+0%12=0.0083309
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1.3%12=0.00108333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,850.00−$150.00+0.0083309×$60,000.00(0.0083309+0.00108333)=$339,895.38
  6. 6. Maximum home price: $448,140.62

    1. Find your monthly income before tax: yearly income ÷ 12

      $120,000.0012=$10,000.00
    2. Housing limit: up to 26% of your monthly income can go to housing

      $10,000.00×26%=$2,600.00
    3. Total debt limit: 32% of your monthly income, minus what your other debts already take

      $10,000.00×32%−$560.00=$2,640.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,600.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00561531+0%12=0.00561531
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1%12=0.00083333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,600.00−$131.25+0.00561531×$75,000.00(0.00561531+0.00083333)=$448,140.62
  7. 7. Maximum home price: $470,148.94

    1. Find your monthly income before tax: yearly income ÷ 12

      $125,000.0012=$10,416.67
    2. Housing limit: up to 36% of your monthly income can go to housing

      $10,416.67×36%=$3,750.00
    3. Total debt limit: 38% of your monthly income, minus what your other debts already take

      $10,416.67×38%−$600.00=$3,358.33
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the total debt limit)

      H=$3,358.33
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00704941+0%12=0.00704941
    6. Find b: how much each $1 of home price adds in property tax each month

      b=0.9%12=0.00075
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$3,358.33−$79.17+0.00704941×$55,000.00(0.00704941+0.00075)=$470,148.94
  8. 8. Maximum home price: $369,424.48

    1. Find your monthly income before tax: yearly income ÷ 12

      $120,000.0012=$10,000.00
    2. Housing limit: up to 28% of your monthly income can go to housing

      $10,000.00×28%=$2,800.00
    3. Total debt limit: 45% of your monthly income, minus what your other debts already take

      $10,000.00×45%−$500.00=$4,000.00
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,800.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00733765+0%12=0.00733765
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1%12=0.00083333
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,800.00−$166.67+0.00733765×$52,500.00(0.00733765+0.00083333)=$369,424.48
  9. 9. Maximum home price: $319,883.88

    1. Find your monthly income before tax: yearly income ÷ 12

      $110,000.0012=$9,166.67
    2. Housing limit: up to 30% of your monthly income can go to housing

      $9,166.67×30%=$2,750.00
    3. Total debt limit: 38% of your monthly income, minus what your other debts already take

      $9,166.67×38%−$660.00=$2,823.33
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,750.00
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00843857+0%12=0.00843857
    6. Find b: how much each $1 of home price adds in property tax each month

      b=1.4%12=0.00116667
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,750.00−$150.00+0.00843857×$56,000.00(0.00843857+0.00116667)=$319,883.88
  10. 10. Maximum home price: $362,725.79

    1. Find your monthly income before tax: yearly income ÷ 12

      $130,000.0012=$10,833.33
    2. Housing limit: up to 20% of your monthly income can go to housing

      $10,833.33×20%=$2,166.67
    3. Total debt limit: 35% of your monthly income, minus what your other debts already take

      $10,833.33×35%−$500.00=$3,291.67
    4. You have to stay under both limits, so the lower one sets your housing budget H (here, the housing limit)

      H=$2,166.67
    5. Find a: how much each $1 you borrow adds to your monthly payment, including any PMI

      a=0.00599551+0%12=0.00599551
    6. Find b: how much each $1 of home price adds in property tax each month

      b=0.9%12=0.00075
    7. Work backward from your budget H to the highest price whose loan, tax, insurance and HOA fit inside it

      price=$2,166.67−$139.58+0.00599551×$70,000.00(0.00599551+0.00075)=$362,725.79