2. Although the shop is new, research has shown that in order to keep it looking professional, it will have to be renovated in 3 years' time. Sibusiso got some quotes and discovered that it would cost them approximately R30 000,00 to do the renovations according to this year's prices. Sibusiso has a fixed deposit that will mature in 3 years' time, at a value of R35 000. Will Sibusiso's fixed deposit investment be able to cover the costs of the shop renovations in 3 years' time, if inflation remains constant at 6.8\% p.a.?

Below is a step‐by‐step solution in markdown using LaTeX for the mathematical formulas. --- ### Step 1. Identify the current renovation cost The quotation given is: \[ \text{Current Cost} = \text{R}30\,000 \] --- ### Step 2. Calculate the cost in 3 years with inflation Since the renovation cost today will increase due to inflation, we use the formula for compound interest/inflation: \[ \text{Future Cost} = \text{Present Cost} \times (1 + i)^n \] where: - \( i = 0.068 \) (annual inflation rate of 6.8%) - \( n = 3 \) (number of years) Thus, the future renovation cost is: \[ \text{Future Cost} = \text{R}30\,000 \times (1.068)^3 \] --- ### Step 3. Evaluate \((1.068)^3\) We calculate: \[ (1.068)^3 \approx 1.068 \times 1.068 \times 1.068 \approx 1.218 \] *(The value is rounded to three decimal places.)* Now, the inflated cost becomes: \[ \text{Future Cost} \approx \text{R}30\,000 \times 1.218 \approx \text{R}36\,540 \] --- ### Step 4. Compare the future renovation cost to the fixed deposit Sibusiso's fixed deposit will mature to: \[ \text{Fixed Deposit} = \text{R}35\,000 \] Comparing the two: - **Future renovation cost:** \(\approx \text{R}36\,540\) - **Fixed deposit:** \(\text{R}35\,000\) --- ### Step 5. Conclusion Since: \[ \text{R}36\,540 > \text{R}35\,000, \] Sibusiso's fixed deposit will **not** be sufficient to cover the renovation cost in 3 years if inflation remains constant at 6.8% per annum. ---