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A course at university costs R10 000 rand. If a father wishes to do this in five years time, what will it cost him if the rate of inflation is estimated to be 11.5% p.a.?

Mathematics

ScanSolve AI Answer

Answer

R17 200.90\text{R17 200.90}

Step-by-step solution

4 steps
  1. Identify the given values.

    The current cost of the course (Present Value, PVPV) is R10 000.
    The time period (nn) is 5 years.
    The annual inflation rate (ii) is 11.5%.

  2. Convert the inflation rate to a decimal.

    i=11.5100=0.115i = \frac{11.5}{100} = 0.115
  3. Use the future value formula to calculate the cost after 5 years.

    The formula for future value with compound inflation is:

    FV=PV(1+i)nFV = PV (1 + i)^n

    Substitute the given values into the formula:

    FV=10000(1+0.115)5FV = 10000 (1 + 0.115)^5 FV=10000(1.115)5FV = 10000 (1.115)^5
  4. Calculate the future value.

    FV=10000×1.7200896FV = 10000 \times 1.7200896 FV=17200.896FV = 17200.896

    Rounding to two decimal places for currency:

    FV=17200.90FV = 17200.90

    The course will cost R17 200.90 in five years time.

    R17 200.90\text{R17 200.90}
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