Unit F: Finance

Practice


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  1. Rosalita buys a $39 384.00 van at an annual interest rate of 8%. Her monthly payment is $650.00.

    1. Determine the number payments Rosalita will make during the loan.



    2. How long will it take for Rosalita to pay off the loan? Express the answer in years.

  2. Jessica purchases a new car for $25 000.00 with an interest rate of 4.5% for a 5 year term.

    1. What is Jessica's monthly payment?

    2. What is the total amount that Jessica pays for the car?
    3. How much interest does Jessica pay on the car loan?

  3. Nadeem purchased a new SUV from a dealership for $36 845.00 before GST. He made a down payment of $8 000.00. Nadeem received a loan for 5.5 years at a rate of 9.5%.

    1. What is the total price of the SUV including GST?
    2. What is the total amount of the loan for the SUV?
    3. Calculate the monthly payment.

    4. How much interest did Nadeem pay on the loan?
    5. How much value did Nadeem's SUV lose due to depreciation if his SUV is worth $15 000.00 after 5.5 years? Use the answer to part a as the initial price.
    6. Calculate the depreciation per year.

  4. When Michael returned a car after a 48 month lease, the odometer reading was 26 112 km. The kilometre allowance for the lease is 24 000 km. If the cost per excess kilometre is $0.26, what penalty will Michael need to pay for exceeding the kilometre allowance?
Rosalita buys a $39 384.00 van at an annual interest rate of 8%. Her monthly payment is $650.00.

  1. Determine the number payments Rosalita will make during the loan.



  2. How long will it take for Rosalita to pay off the loan? Express the answer in years.


  1. Record the information in a chart.

    principal 39 384.00
    annual interest rate
    		 8
    monthly payment
    		 650.00

    Now, enter these values into the Number of Monthly Payments Calculator. Click to find the number of monthly payments.

    Rosalita will make 78 payments.

  2. To find the length of time to pay off the loan, convert 78 months to years.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»78«/mn»«mo»§#160;«/mo»«mi»months«/mi»«mo»§#215;«/mo»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»year«/mi»«/mrow»«mrow»«mn»12«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»6«/mn»«mo».«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»years«/mi»«/math»

    Rosalita will pay off the van in 6.5 years.
Jessica purchases a new car for $25 000.00 with an interest rate of 4.5 % for a 5 year term.

  1. What is Jessica's monthly payment?


  2. What is the total amount that Jessica pays for the car?
  3. How much interest does Jessica pay on the car loan?


  1. To use the Monthly Payment Calculator, the principal, annual interest rate, and number of monthly payments must be known. Record the information in a chart.

    principal 25 000.00
    annual interest rate
    		 4.5
    number of monthly payments
    		 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«mo»§#160;«/mo»«mi»years«/mi»«mo»§#215;«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»year«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»60«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/math»

    Substitute the values from the chart into the Monthly Payment Calculator and then click to find the monthly payment.

    Jessica's monthly payment is $466.08.

  2. To find the total amount Jessica pays for the car, multiply the monthly payment by the number of monthly payments. The total amount that Jessica pays for the car loan is

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»a«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»monthly«/mi»«mo»§#160;«/mo»«mi»payment«/mi»«mo»§#215;«/mo»«mi»number«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»monthly«/mi»«mo»§#160;«/mo»«mi»payments«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»466«/mn»«mo».«/mo»«mn»08«/mn»«mo»/«/mo»«mi»month«/mi»«mo»§#215;«/mo»«mn»60«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»27«/mn»«mo»§#160;«/mo»«mn»964«/mn»«mo».«/mo»«mn»80«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Jessica pays a total of $27 964.80 for the car.

  3. In a loan, the interest is the amount of money paid above the original price of the vehicle.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»interest«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«mo»-«/mo»«mi»initial«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»27«/mn»«mo»§#160;«/mo»«mn»964«/mn»«mo».«/mo»«mn»80«/mn»«mo»-«/mo»«mo»$«/mo»«mn»25«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo».«/mo»«mn»00«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mn»964«/mn»«mo».«/mo»«mn»80«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Jessica paid $2 964.80 in interest on the car loan.
Nadeem purchased a new SUV from a dealership for $36 845.00 before GST. He made a down payment of $8 000.00. Nadeem received a loan for 5.5 years at a rate of 9.5%.

  1. What is the total price of the SUV including GST?
  2. What is the total amount of the loan for the SUV?
  3. Calculate the monthly payment.


  4. How much interest did Nadeem pay on the loan?
  5. How much value did Nadeem's SUV lose due to depreciation if his SUV is worth $15 000.00 after 5.5 years? Use the answer to part a as the initial price.
  6. Calculate the depreciation per year.


  1. The total price can be found by multiplying the price of the SUV by the GST of 5% and then adding that amount to the price.

    A simpler way to calculate the total price is to multiply the price by 1.05.

    $36 845 × 1.05 = $38 687.25

    The total price of the SUV is $38 687.25.

  2. The loan is equal to the total price less the down payment.

    $38 687.25 – $8 000.00 = $30 687.25

    The loan amount is $30 687.25.

  3. To use the Monthly Payment Calculator; the principal, annual interest rate, and number of monthly payments must be known. Record the information in a chart.

    principal 30 687.25
    annual interest rate
    		 9.5
    number of monthly payments
    		 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«mo».«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»years«/mi»«mo»§#215;«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»year«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/math»

    Substitute the values from the chart into the Monthly Payment Calculator and then click to find the monthly payment.

    Nadeem's monthly payment is $598.76.

  4. Step 1: Find the total amount that Nadeem paid for the SUV.

    The total amount that Nadeem paid for the SUV is equal to the sum of the down payment and the amount of the loan.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»amount«/mi»«mo»§#160;«/mo»«mi»paid«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»down«/mi»«mo»§#160;«/mo»«mi»payment«/mi»«mo»+«/mo»«mi»total«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»8«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo».«/mo»«mn»00«/mn»«mo»+«/mo»«mfenced»«mrow»«mo»$«/mo»«mn»598«/mn»«mo».«/mo»«mn»76«/mn»«mo»/«/mo»«mi»month«/mi»«mo»§#215;«/mo»«mn»66«/mn»«mo»§#160;«/mo»«mi»months«/mi»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»8«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo».«/mo»«mn»00«/mn»«mo»+«/mo»«mo»$«/mo»«mn»39«/mn»«mo»§#160;«/mo»«mn»518«/mn»«mo».«/mo»«mn»16«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»47«/mn»«mo»§#160;«/mo»«mn»518«/mn»«mo».«/mo»«mn»16«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Nadeem paid a total of $47 518.16 for the SUV.

    Step 2: Calculate the amount of interest paid.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»interest«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mi»total«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«mo»-«/mo»«mi»initial«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»loan«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»47«/mn»«mo»§#160;«/mo»«mn»518«/mn»«mo».«/mo»«mn»16«/mn»«mo»-«/mo»«mo»$«/mo»«mn»38«/mn»«mo»§#160;«/mo»«mn»687«/mn»«mo».«/mo»«mn»25«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»8«/mn»«mo»§#160;«/mo»«mn»830«/mn»«mo».«/mo»«mn»91«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Nadeem paid $8 830.91 in interest on the loan.

  5. The depreciation over 5.5 years can be found by subtracting the present value of the SUV from the initial cost of the SUV.

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»initial«/mi»«mo»§#160;«/mo»«mi»cost«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»SUV«/mi»«mo»-«/mo»«mi»present«/mi»«mo»§#160;«/mo»«mi»value«/mi»«mo»§#160;«/mo»«mi»of«/mi»«mo»§#160;«/mo»«mi»the«/mi»«mo»§#160;«/mo»«mi»SUV«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»38«/mn»«mo»§#160;«/mo»«mn»687«/mn»«mo».«/mo»«mn»25«/mn»«mo»-«/mo»«mo»$«/mo»«mn»15«/mn»«mo»§#160;«/mo»«mn»000«/mn»«mo».«/mo»«mn»00«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»23«/mn»«mo»§#160;«/mo»«mn»687«/mn»«mo».«/mo»«mn»25«/mn»«/mtd»«/mtr»«/mtable»«/math»

    Nadeem's SUV lost $23 687.25 in value due to depreciation.

  6. To calculate the depreciation per year, divide the depreciation amount by the number of years. The depreciation per year is

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»$«/mo»«mn»23«/mn»«mo»§#160;«/mo»«mn»687«/mn»«mo».«/mo»«mn»25«/mn»«/mrow»«mrow»«mn»5«/mn»«mo».«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»years«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»$«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mn»306«/mn»«mo».«/mo»«mn»77«/mn»«/math»

    Nadeem's SUV depreciated $4 306.77 per year.
When Michael returned a car after a 48 month lease, the odometer reading was 26 112 km. The kilometre allowance for the lease is 24 000 km. If the cost per excess kilometre is $0.26, what penalty will Michael need to pay for exceeding the kilometre allowance?

The extra kilometres driven is equal to the difference between the number of kilometres driven and the kilometre allowance of 20 000 kilometres.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»extra«/mi»«mo»§#160;«/mo»«mi»kilometres«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»26«/mn»«mo»§#160;«/mo»«mn»112«/mn»«mo»-«/mo»«mn»24«/mn»«mo»§#160;«/mo»«mn»000«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»2«/mn»«mo»§#160;«/mo»«mn»112«/mn»«/mtd»«/mtr»«/mtable»«/math»

Michael exceeded the limit by 2 112 km. Multiply this value by the cost per extra kilometre.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mi»penalty«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mi»cost«/mi»«mi»km«/mi»«/mfrac»«mo»§#215;«/mo»«mi»extra«/mi»«mo»§#160;«/mo»«mi»km«/mi»«mo»§#160;«/mo»«mi»driven«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»0«/mn»«mo».«/mo»«mn»26«/mn»«mo»§#215;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mn»112«/mn»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»$«/mo»«mn»549«/mn»«mo».«/mo»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/math»

Michael will pay a penalty of $549.12 when he returns the car at the end of the lease.