CPAN112 – Fundamentals of Numeric Computing – Final Term

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Fundamentals of Numeric Computing

CPAN 112

Final Term TEST

Please read the following instruction very carefully before answering any questions:

  • Please read all the questions very carefully.
  • Please provide your answers in the boxes below each question, and do not change the text colour.
  • Your answer MUST show the solution procedure. There is no credit if you only state the final answer.
  • Please highlight your final answer to each question.
  • Please keep the naming conventions requested in this lab and each question.
  • Once you complete your lab, rename your word document file to the (CPAN112_FinalExam_FirstName_LastName). Replace FirstName and LastName with your first name and last name, respectively.

It will be a 10% mark deduction if you do not follow the guidelines mentioned above.

Please show you work using formula’s applied, concept learned and explanation, do not just write the final answer. Feel free to use Python as tool and attach the screenshots.

 

  • A Dining Set is listed for $550.00 less 125/6% (20 5/6%), 10%, 8%
    • What is the net price?
    • How much is the amount of discount allowed?
    • What is the equivalent single rate of discount that was allowed?
    • Discounts:
      20 5/6% = 125/6% ÷ 100 = 125/600 = 0.208333
      10% = 10 ÷ 100 = 0.1
      8% = 8 ÷ 100 = 0.08

      Listed price: 550.00

      First discount: 550 – (550 * 0.208333) = 435.417

      Second discount: 435.417 – (435.417 * 0.1) = 391.875

      Third discount: 391.875 – (391.875 * 0.08) = 360.525

      The net price is approximately $360.53

       

      Discount allowed = Listed price – Net price
      Discount allowed =  550.00 – 360.53 = 189.47

      The amount of discount allowed is $189.47.

       

      Equivalent single rate of discount = 1 – (1 – d1) * (1 – d2) * (1 – d3)
           d represent Discount
      1 – (1 – 0.208333) * (1 – 0.1) * (1 – 0.08)
      1 – 0.791667 * 0.9 * 0.92
      1 – 0.654075 = 0.345925
      i.e. 34.59%

      Equivalent single rate of discount = 34.59%
a.) $360.53  ||  b.) $189.47  ||  c.) 34.59%

 

  • The ABC Company received a $959 invoice with terms 3/15, n/30. The firm could not pay the entire bill within ten days but sent a check for $400 within the first 15 days. What amount should be credited to the ABC Company.
    • Since ABC Company made a partial payment of $400 within the first 15 days, they are eligible for the 3% discount.
      Calculate the discount on the partial payment.
      Discount = 400 * 3% = 12
      Credited amount = $400 + $12 = 412
      The amount that should be credited is $412.
$412

 

  • What rate of interest did you receive over a period of 80 days if your principal was $7000 and it has a maturity value of $7700?
    • Interest = Principle x Rate x Time
      7700-7000 = 7000 x  R x 80 / 365
      700 = 7000 x R x 0.22
      700/7000*0.22 = R
      0.4545 = R
Rate of Interest = 45.45%

 

  • A loan payment of $2100 was due 60 days ago and another payment of $2200 is due 45 days from now. What single payment 90 days from now will pay off the two obligation if interest is to be 11% and the agreed focal date is 90 days from now?
    • Interest = 0.11

      Calculate the interest for each payment based on the focal date, which is 90 days from now:

      For $2100 payment that was due 60 days ago, it will add interest for 60 + 90 = 150 days. i.e. 0.410958 year
      For $2200 payment that is due 45 days from now, it will add interest for 90 – 45 = 45 days. i.e. 0.123288 year

      Future Value = Principal × (1 + Interest Rate × Time)

      For the $2100 payment:
      FV1 = 2100 * (1 + 0.11 * 0.410958) = $2194.93 approx.

      For the $2200 payment:
      FV2 = 2200 * (1 + 0.11 * 0.123288) = $2231.14 approx.

      Single Payment = FV1 + FV2
      Single Payment = 2194.93 + 2231.14
Simgle Payment = $4426.07

 

  • A debt of $6020 is to be settled by two equal payments due today, and three years from now respectively. Determine the size of the equal payments if money is worth 9.73% and the agreed focal day is today.
    • PV = P * (1 – (1 + r)^(-n)) / r

      P = PV * r / (1 – (1 + r)^(-n))

      P = 6020 * 0.0973 / (1 – (1 + 0.0973)^(-2))

      P=3456.103

 

  • To what future value will a principal of $8000.00 amount in three years at 7.5% p.a.compounded:
  1. annually
  2. semi-annually
  3. quarterly
  4. monthly
  • FV = P * (1 + r/n)^(nt)

    a.) compounded annually
    FV = 8000 * (1 + 0.075/1)^(1*3)

    FV = $9938.375

     

    b.) semi-annually
    FV = 8000 * (1 + 0.075/2)^(2*3)
    FV= $9977.43

     

    c.) quarterly

    FV = 8000 * (1 + 0.075/4)^(4*3)
    FV = $9997.73

     

    d.) monthly
    FV = 8000 * (1 + 0.075/12)^(12*3)
    FV = $10011.57
a.) $9938.375

b.) $9977.43

c.) $9997.73

d.) $10011.57

 

  • Fred started RSP plan for his kid on January 1, 2020, with a deposit of $1000. He added $2000 on January 1, 2021, and $3000 on January 1, 2022. What is the accumulated value of his RSP account on July 1, 2022, if interest is 10.55% compounded quarterly?
    • PV = FV / (1 + r / n)^nt
      FV = PV * (1 + r / n)^ntFuture value of the deposit made on January 1, 2020:
      from January 1, 2020, to July 1, 2022 = 2.5 years
      FV1 = 1000 * (1 + 0.1055/4)^(4 * 2.5)
      FV1 = $1297.36

      Future value of the deposit made on January 1, 2021:
      from January 1, 2021, to July 1, 2022 = 1.5 years
      FV2 = 2000 * (1 + 0.1055/4)^(4 * 1.5)
      FV2 = 2338.12

      Future value of the deposit made on January 1, 2022:
      from January 1, 2022, to July 1, 2022 = 0.5 years
      FV3 = 3000 * (1 + 0.1055/4)^(4 * 0.5)
      FV3 = 3160.34

      Total Value is FV1 + FV2 + FV3
      i.e. 1297.36 + 2338.12 + 3160.34
      Accumualated Value = $6795.82
$6795.82 approx

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