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Grade 12 · Financial Maths
Annuities & Loan Repayments (Grade 12)
MEMORANDUM
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  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    R1 500 is deposited monthly for 20 years at 9% p.a. compounded monthly. Determine the future value.
    (2)
    i = 0,0075, n = 240 → F = R1001830,30✓✓ (2)
  2. 2
    How much was actually deposited in total in that annuity?
    (2)
    240 × 1 500 = R360 000✓✓ (2)
  3. 3
    A bond of R800 000 is repaid monthly over 20 years at 9% p.a. compounded monthly. Determine the monthly instalment.
    (2)
    x = 800 000 × 0,00751 − (1,0075)−240 = R7197,81✓✓ (2)
  4. 4
    Determine the outstanding balance on that bond after 5 years.
    (2)
    PV of the remaining 180 payments = R709656,39✓✓ (2)
  5. 5
    Write down the value of i for 9% p.a. compounded monthly.
    (2)
    0,0912 = 0,0075✓✓ (2)
  6. 6
    Which formula do you use when saving towards a future amount?
    (2)
    Future value, F = x[(1+i)n − 1]i✓✓ (2)
  7. 7
    Which formula do you use for a loan taken out today?
    (2)
    Present value, P = x[1 − (1+i)−n]i✓✓ (2)
  8. 8
    How is the outstanding balance on a loan calculated?
    (2)
    As the present value of the payments still outstanding.✓✓ (2)
TOTAL: 16 marks
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