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Mathematics of Finance

Module by: Vishnu Naidoo. E-mail the author

Summary: Mathematics of Finance Grade 12 Fixed Payments and Balance

Vishnu Naidoo

Mathematics Test: Mathematics of Finance /Linear Programming: Marks (50)

  1. Determine the effective rate of interest if the nominal rate is 8,9% pa compounded monthly. (3)
  2. Determine the nominal rate of interest if the effective rate of interest is 11,7% pa compounded daily(one year = 365 days). (3)
  3. Mrs Gumede purchased a house for R1 200 000 in a golf estate. She decided to pay a fixed amount of R15 000 per month at an interest rate of 8,9% p.a compounded monthly.
    1. Determine the number of payments. (5)
    2. Hence determine the final payment. (5)
  4. A company purchased the state of the art printing machine for R800 000.

This machine depreciates at a rate of 10% p.a on diminishing balance.

This company decided to replace this machine in 5 years time.

The new machine appreciates in value at a rate of 9% p.a compounded annually.

    1. Determine the value of the old machine in 5 years time.(3)
    2. Determine the value of the new printing machine in 5 years time.(3)
    3. A sinking fund was set up. What amount must the sinking fund achieve in 5 years time? (2)
    4. Determine the monthly payment into the sinking fund if the sinking fund is set up 6 months after the purchase of the machine and if interest is quoted at 10,8%p.a. compounded monthly. (5)
    5. The company took a decision to withdraw R10 000 every 3 months after the sinking fund was set up and finish 6 months prior to the purchase of the new machine then determine the new monthly instalments into the sinking fund. (5)
  2. A company manufactured one kilolitre and five kilolitre water tanks. The one kl tank requires 3 units of labour whilst the five kl require 8 units of labour. The company has 2400 units of labour per week. The machining time on the one kl tank is 10 units and that of the five kl tank is 10 units. The company has 4000 units of machining time. The profit on the five kl is R1000 whilst the profit on the one kl is R300. There is an order of at least 100 one kl tanks and 150 five kl tanks.

5.1 Write down the constraints if ‘x’ represents the number of one kl tanks and ‘y’ represents the number of five kl tanks. (8)

5.2 Draw the graphs of the constraints showing clearly the feasible region. (6)

5.3 Determine the objective function and draw the optimum search line.2

5.4 Determine the number of one kl and five kl tanks that must be manufactured to optimise profits and the maximum profit. (4)

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