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Reverse Mortgage worksheet

Grade 7 · CCSS 7.RP.A.3

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

  1. Problem 1.
    • Home value: $350,000
    • Age of the youngest borrower: 85 years
    • Expected interest rate: 6%
    • Mortgages to pay off: $65,000
    • Other closing costs: $2,600

    Find: Estimated principal limit

  2. Problem 2.
    • Home value: $320,000
    • Age of the youngest borrower: 68 years
    • Expected interest rate: 7.5%
    • Mortgages to pay off: $40,000
    • Other closing costs: $3,200

    Find: Estimated principal limit

  3. Problem 3.
    • Home value: $480,000
    • Age of the youngest borrower: 78 years
    • Expected interest rate: 6%
    • Mortgages to pay off: $70,000
    • Other closing costs: $2,400

    Find: Estimated principal limit

  4. Problem 4.
    • Home value: $390,000
    • Age of the youngest borrower: 68 years
    • Expected interest rate: 5.5%
    • Mortgages to pay off: $65,000
    • Other closing costs: $3,000

    Find: Estimated principal limit

  5. Problem 5.
    • Home value: $550,000
    • Age of the youngest borrower: 85 years
    • Expected interest rate: 7.5%
    • Mortgages to pay off: $50,000
    • Other closing costs: $4,000

    Find: Estimated principal limit

  6. Problem 6.
    • Home value: $440,000
    • Age of the youngest borrower: 85 years
    • Expected interest rate: 5.5%
    • Mortgages to pay off: $47,500
    • Other closing costs: $3,200

    Find: Estimated principal limit

  7. Problem 7.
    • Home value: $460,000
    • Age of the youngest borrower: 68 years
    • Expected interest rate: 7.5%
    • Mortgages to pay off: $52,500
    • Other closing costs: $2,100

    Find: Estimated principal limit

  8. Problem 8.
    • Home value: $420,000
    • Age of the youngest borrower: 72 years
    • Expected interest rate: 6.75%
    • Mortgages to pay off: $55,000
    • Other closing costs: $3,400

    Find: Estimated principal limit

  9. Problem 9.
    • Home value: $375,000
    • Age of the youngest borrower: 85 years
    • Expected interest rate: 5.5%
    • Mortgages to pay off: $70,000
    • Other closing costs: $2,000

    Find: Estimated principal limit

  10. Problem 10.
    • Home value: $425,000
    • Age of the youngest borrower: 85 years
    • Expected interest rate: 7.5%
    • Mortgages to pay off: $60,000
    • Other closing costs: $2,250

    Find: Estimated principal limit

Answer key: Reverse Mortgage worksheet

  1. 1. Estimated principal limit: $192,150.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$350,000.00
    2. Look up HUD's factor for age 85. Your rate is rounded to the nearest 1/8 of a percent first

      6% rounds to=6%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $350,000.00×0.549=$192,150.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $350,000.00×2%=$7,000.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $7,000.00+$5,500.00+$2,600.00+$65,000.00=$80,100.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $192,150.00−$80,100.00=$112,050.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $192,150.00×60%=$115,290.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $115,290.00−$80,100.00=$35,190.00
  2. 2. Estimated principal limit: $107,520.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$320,000.00
    2. Look up HUD's factor for age 68. Your rate is rounded to the nearest 1/8 of a percent first

      7.5% rounds to=7.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $320,000.00×0.336=$107,520.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $320,000.00×2%=$6,400.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $6,400.00+$5,200.00+$3,200.00+$40,000.00=$54,800.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $107,520.00−$54,800.00=$52,720.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here the second is larger, and it can't pass the limit

      $54,800.00+$107,520.00×10%=$65,552.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $65,552.00−$54,800.00=$10,752.00
  3. 3. Estimated principal limit: $226,080.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$480,000.00
    2. Look up HUD's factor for age 78. Your rate is rounded to the nearest 1/8 of a percent first

      6% rounds to=6%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $480,000.00×0.471=$226,080.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $480,000.00×2%=$9,600.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $9,600.00+$6,000.00+$2,400.00+$70,000.00=$88,000.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $226,080.00−$88,000.00=$138,080.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $226,080.00×60%=$135,648.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $135,648.00−$88,000.00=$47,648.00
  4. 4. Estimated principal limit: $166,140.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$390,000.00
    2. Look up HUD's factor for age 68. Your rate is rounded to the nearest 1/8 of a percent first

      5.5% rounds to=5.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $390,000.00×0.426=$166,140.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $390,000.00×2%=$7,800.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $7,800.00+$5,900.00+$3,000.00+$65,000.00=$81,700.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $166,140.00−$81,700.00=$84,440.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $166,140.00×60%=$99,684.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $99,684.00−$81,700.00=$17,984.00
  5. 5. Estimated principal limit: $271,150.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$550,000.00
    2. Look up HUD's factor for age 85. Your rate is rounded to the nearest 1/8 of a percent first

      7.5% rounds to=7.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $550,000.00×0.493=$271,150.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $550,000.00×2%=$11,000.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $11,000.00+$6,000.00+$4,000.00+$50,000.00=$71,000.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $271,150.00−$71,000.00=$200,150.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $271,150.00×60%=$162,690.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $162,690.00−$71,000.00=$91,690.00
  6. 6. Estimated principal limit: $250,800.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$440,000.00
    2. Look up HUD's factor for age 85. Your rate is rounded to the nearest 1/8 of a percent first

      5.5% rounds to=5.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $440,000.00×0.57=$250,800.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $440,000.00×2%=$8,800.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $8,800.00+$6,000.00+$3,200.00+$47,500.00=$65,500.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $250,800.00−$65,500.00=$185,300.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $250,800.00×60%=$150,480.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $150,480.00−$65,500.00=$84,980.00
  7. 7. Estimated principal limit: $154,560.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$460,000.00
    2. Look up HUD's factor for age 68. Your rate is rounded to the nearest 1/8 of a percent first

      7.5% rounds to=7.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $460,000.00×0.336=$154,560.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $460,000.00×2%=$9,200.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $9,200.00+$6,000.00+$2,100.00+$52,500.00=$69,800.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $154,560.00−$69,800.00=$84,760.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $154,560.00×60%=$92,736.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $92,736.00−$69,800.00=$22,936.00
  8. 8. Estimated principal limit: $160,860.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$420,000.00
    2. Look up HUD's factor for age 72. Your rate is rounded to the nearest 1/8 of a percent first

      6.75% rounds to=6.75%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $420,000.00×0.383=$160,860.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $420,000.00×2%=$8,400.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $8,400.00+$6,000.00+$3,400.00+$55,000.00=$72,800.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $160,860.00−$72,800.00=$88,060.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $160,860.00×60%=$96,516.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $96,516.00−$72,800.00=$23,716.00
  9. 9. Estimated principal limit: $213,750.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$375,000.00
    2. Look up HUD's factor for age 85. Your rate is rounded to the nearest 1/8 of a percent first

      5.5% rounds to=5.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $375,000.00×0.57=$213,750.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $375,000.00×2%=$7,500.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $7,500.00+$5,750.00+$2,000.00+$70,000.00=$85,250.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $213,750.00−$85,250.00=$128,500.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $213,750.00×60%=$128,250.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $128,250.00−$85,250.00=$43,000.00
  10. 10. Estimated principal limit: $209,525.00

    1. HUD counts the home's value here, because it's under the national limit for 2026

       limit$1,249,125.00= value counted$425,000.00
    2. Look up HUD's factor for age 85. Your rate is rounded to the nearest 1/8 of a percent first

      7.5% rounds to=7.5%
    3. Multiply by the factor to get your principal limit, the most this loan can start with

      $425,000.00×0.493=$209,525.00
    4. Find the upfront mortgage insurance: 2% of the value counted

      $425,000.00×2%=$8,500.00
    5. Add what must be paid at closing: insurance, the highest allowed origination fee, other costs and any mortgage payoff

      $8,500.00+$6,000.00+$2,250.00+$60,000.00=$76,750.00
    6. Subtract those from the principal limit. This is what's left for you, in total

      $209,525.00−$76,750.00=$132,775.00
    7. In the first year, you can use the greater of 60% of the limit, or the closing items plus 10% of the limit. Here 60% is larger

      $209,525.00×60%=$125,715.00
    8. Subtract the closing items to see the cash you could use in the first 12 months

      $125,715.00−$76,750.00=$48,965.00