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Car 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: $22,500
    • Current interest rate: 9%
    • Months left on current loan: 60 months
    • New interest rate: 5%
    • New loan term: 36 months
    • Refinance fees: $220
    • How fees are paid: Added to the new loan
    • What the car is worth today: $22,000

    Find: Monthly savings

  2. Problem 2.
    • Current loan balance: $24,000
    • Current interest rate: 10%
    • Months left on current loan: 48 months
    • New interest rate: 7.4%
    • New loan term: 72 months
    • Refinance fees: $240
    • How fees are paid: Paid in cash
    • What the car is worth today: $24,000

    Find: Monthly savings

  3. Problem 3.
    • Current loan balance: $22,000
    • Current interest rate: 10.5%
    • Months left on current loan: 48 months
    • New interest rate: 8%
    • New loan term: 72 months
    • Refinance fees: $250
    • How fees are paid: Paid in cash
    • What the car is worth today: $25,000

    Find: Monthly savings

  4. Problem 4.
    • Current loan balance: $25,000
    • Current interest rate: 8.5%
    • Months left on current loan: 36 months
    • New interest rate: 5.75%
    • New loan term: 36 months
    • Refinance fees: $350
    • How fees are paid: Added to the new loan
    • What the car is worth today: $24,000

    Find: Monthly savings

  5. Problem 5.
    • Current loan balance: $18,500
    • Current interest rate: 7%
    • Months left on current loan: 24 months
    • New interest rate: 5.5%
    • New loan term: 48 months
    • Refinance fees: $460
    • How fees are paid: Added to the new loan
    • What the car is worth today: $22,000

    Find: Monthly savings

  6. Problem 6.
    • Current loan balance: $20,000
    • Current interest rate: 9.6%
    • Months left on current loan: 24 months
    • New interest rate: 5%
    • New loan term: 48 months
    • Refinance fees: $400
    • How fees are paid: Added to the new loan
    • What the car is worth today: $19,500

    Find: Monthly savings

  7. Problem 7.
    • Current loan balance: $26,000
    • Current interest rate: 6.8%
    • Months left on current loan: 24 months
    • New interest rate: 5.5%
    • New loan term: 60 months
    • Refinance fees: $300
    • How fees are paid: Paid in cash
    • What the car is worth today: $29,500

    Find: Monthly savings

  8. Problem 8.
    • Current loan balance: $20,000
    • Current interest rate: 10%
    • Months left on current loan: 36 months
    • New interest rate: 5.75%
    • New loan term: 60 months
    • Refinance fees: $225
    • How fees are paid: Paid in cash
    • What the car is worth today: $20,000

    Find: Monthly savings

  9. Problem 9.
    • Current loan balance: $22,000
    • Current interest rate: 7%
    • Months left on current loan: 36 months
    • New interest rate: 5%
    • New loan term: 72 months
    • Refinance fees: $240
    • How fees are paid: Paid in cash
    • What the car is worth today: $25,000

    Find: Monthly savings

  10. Problem 10.
    • Current loan balance: $26,000
    • Current interest rate: 6.6%
    • Months left on current loan: 24 months
    • New interest rate: 5.4%
    • New loan term: 36 months
    • Refinance fees: $325
    • How fees are paid: Paid in cash
    • What the car is worth today: $31,500

    Find: Monthly savings

Answer key: Car Refinance worksheet

  1. 1. Monthly savings: -$213.88

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 60 months, where the monthly rate is the yearly rate ÷ 12

      $22,500.00×0.00751−(1+0.0075)−60=$467.06
    2. Add the fees to what you borrow, since they go into the new loan

      $22,500.00+$220.00=$22,720.00
    3. Find the new payment. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $22,720.00×0.004166671−(1+0.00416667)−36=$680.94
    4. Subtract the new payment from the current one to see your monthly savings

      $467.06−$680.94=−$213.88
    5. The new payment isn't lower, so there are no monthly savings to pay back the fees

    6. Add up everything left to pay on the current loan

      $467.06×60=$28,023.78
    7. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $680.94×36+$0.00=$24,513.80
    8. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $28,023.78−$24,513.80=$3,509.98
    9. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $22,720.00$22,000.00=103.27%
  2. 2. Monthly savings: $194.90

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 48 months, where the monthly rate is the yearly rate ÷ 12

      $24,000.00×0.008333331−(1+0.00833333)−48=$608.70
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 72 months, where the monthly rate is the yearly rate ÷ 12

      $24,000.00×0.006166671−(1+0.00616667)−72=$413.80
    3. Subtract the new payment from the current one to see your monthly savings

      $608.70−$413.80=$194.90
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $240.00$194.90=2 months
    5. Add up everything left to pay on the current loan

      $608.70×48=$29,217.70
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $413.80×72+$240.00=$30,033.71
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $29,217.70−$30,033.71=−$816.01
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $24,000.00$24,000.00=100%
  3. 3. Monthly savings: $177.54

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 48 months, where the monthly rate is the yearly rate ÷ 12

      $22,000.00×0.008751−(1+0.00875)−48=$563.27
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 72 months, where the monthly rate is the yearly rate ÷ 12

      $22,000.00×0.006666671−(1+0.00666667)−72=$385.73
    3. Subtract the new payment from the current one to see your monthly savings

      $563.27−$385.73=$177.54
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $250.00$177.54=2 months
    5. Add up everything left to pay on the current loan

      $563.27×48=$27,037.17
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $385.73×72+$250.00=$28,022.65
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $27,037.17−$28,022.65=−$985.48
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $22,000.00$25,000.00=88%
  4. 4. Monthly savings: $20.86

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $25,000.00×0.007083331−(1+0.00708333)−36=$789.19
    2. Add the fees to what you borrow, since they go into the new loan

      $25,000.00+$350.00=$25,350.00
    3. Find the new payment. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $25,350.00×0.004791671−(1+0.00479167)−36=$768.33
    4. Subtract the new payment from the current one to see your monthly savings

      $789.19−$768.33=$20.86
    5. Find the break-even month: divide the fees by your monthly savings, then round up

      $350.00$20.86=17 months
    6. Add up everything left to pay on the current loan

      $789.19×36=$28,410.78
    7. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $768.33×36+$0.00=$27,659.80
    8. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $28,410.78−$27,659.80=$750.98
    9. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $25,350.00$24,000.00=105.62%
  5. 5. Monthly savings: $387.35

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 24 months, where the monthly rate is the yearly rate ÷ 12

      $18,500.00×0.005833331−(1+0.00583333)−24=$828.29
    2. Add the fees to what you borrow, since they go into the new loan

      $18,500.00+$460.00=$18,960.00
    3. Find the new payment. A standard formula finds the one amount that clears the loan in 48 months, where the monthly rate is the yearly rate ÷ 12

      $18,960.00×0.004583331−(1+0.00458333)−48=$440.94
    4. Subtract the new payment from the current one to see your monthly savings

      $828.29−$440.94=$387.35
    5. Find the break-even month: divide the fees by your monthly savings, then round up

      $460.00$387.35=2 months
    6. Add up everything left to pay on the current loan

      $828.29×24=$19,879.03
    7. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $440.94×48+$0.00=$21,165.25
    8. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $19,879.03−$21,165.25=−$1,286.23
    9. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $18,960.00$22,000.00=86.18%
  6. 6. Monthly savings: $449.41

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 24 months, where the monthly rate is the yearly rate ÷ 12

      $20,000.00×0.0081−(1+0.008)−24=$919.21
    2. Add the fees to what you borrow, since they go into the new loan

      $20,000.00+$400.00=$20,400.00
    3. Find the new payment. A standard formula finds the one amount that clears the loan in 48 months, where the monthly rate is the yearly rate ÷ 12

      $20,400.00×0.004166671−(1+0.00416667)−48=$469.80
    4. Subtract the new payment from the current one to see your monthly savings

      $919.21−$469.80=$449.41
    5. Find the break-even month: divide the fees by your monthly savings, then round up

      $400.00$449.41=1 month
    6. Add up everything left to pay on the current loan

      $919.21×24=$22,061.05
    7. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $469.80×48+$0.00=$22,550.28
    8. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $22,061.05−$22,550.28=−$489.23
    9. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $20,400.00$19,500.00=104.62%
  7. 7. Monthly savings: $665.10

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 24 months, where the monthly rate is the yearly rate ÷ 12

      $26,000.00×0.005666671−(1+0.00566667)−24=$1,161.73
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 60 months, where the monthly rate is the yearly rate ÷ 12

      $26,000.00×0.004583331−(1+0.00458333)−60=$496.63
    3. Subtract the new payment from the current one to see your monthly savings

      $1,161.73−$496.63=$665.10
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $300.00$665.10=1 month
    5. Add up everything left to pay on the current loan

      $1,161.73×24=$27,881.55
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $496.63×60+$300.00=$30,097.81
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $27,881.55−$30,097.81=−$2,216.27
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $26,000.00$29,500.00=88.14%
  8. 8. Monthly savings: $261.01

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $20,000.00×0.008333331−(1+0.00833333)−36=$645.34
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 60 months, where the monthly rate is the yearly rate ÷ 12

      $20,000.00×0.004791671−(1+0.00479167)−60=$384.34
    3. Subtract the new payment from the current one to see your monthly savings

      $645.34−$384.34=$261.01
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $225.00$261.01=1 month
    5. Add up everything left to pay on the current loan

      $645.34×36=$23,232.37
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $384.34×60+$225.00=$23,285.12
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $23,232.37−$23,285.12=−$52.75
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $20,000.00$20,000.00=100%
  9. 9. Monthly savings: $324.99

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $22,000.00×0.005833331−(1+0.00583333)−36=$679.30
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 72 months, where the monthly rate is the yearly rate ÷ 12

      $22,000.00×0.004166671−(1+0.00416667)−72=$354.31
    3. Subtract the new payment from the current one to see your monthly savings

      $679.30−$354.31=$324.99
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $240.00$324.99=1 month
    5. Add up everything left to pay on the current loan

      $679.30×36=$24,454.66
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $354.31×72+$240.00=$25,750.21
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $24,454.66−$25,750.21=−$1,295.55
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $22,000.00$25,000.00=88%
  10. 10. Monthly savings: $375.46

    1. Find your current payment from what you owe, your rate and the months left. A standard formula finds the one amount that clears the loan in 24 months, where the monthly rate is the yearly rate ÷ 12

      $26,000.00×0.00551−(1+0.0055)−24=$1,159.38
    2. Find the new payment. A standard formula finds the one amount that clears the loan in 36 months, where the monthly rate is the yearly rate ÷ 12

      $26,000.00×0.00451−(1+0.0045)−36=$783.92
    3. Subtract the new payment from the current one to see your monthly savings

      $1,159.38−$783.92=$375.46
    4. Find the break-even month: divide the fees by your monthly savings, then round up

      $325.00$375.46=1 month
    5. Add up everything left to pay on the current loan

      $1,159.38×24=$27,825.07
    6. Add up everything you'd pay on the new loan, plus any fees paid in cash

      $783.92×36+$325.00=$28,546.17
    7. The difference is your lifetime savings. A negative number means the new loan costs more overall

      $27,825.07−$28,546.17=−$721.09
    8. Compare what you'd owe with what the car is worth. Lenders call this loan-to-value

      $26,000.00$31,500.00=82.54%