Test Your Understanding Answers on page A17 1. A Mercedes VITO could be bought, brand new, for R307 230 in 2013. In 2014 the cost of a new VITO was R321 993 and in 2015 it was R335 730. 1.1 Which year showed the highest inflation rate? 1.2 Calculate the cost of a new VITO in 2016, if inflation was predicted to be at \( 5,4 \% \).

To determine which year showed the highest inflation rate, we need to calculate the inflation rate for each year. The inflation rate can be calculated using the formula: \[ \text{Inflation Rate} = \left( \frac{\text{Current Price}}{\text{Previous Price}} \right) - 1 \] Given: - 2013: R307,230 - 2014: R321,993 - 2015: R335,730 1.1 To find the year with the highest inflation rate, we will calculate the inflation rate for each year and compare them. 1.2 To calculate the cost of a new VITO in 2016 with a predicted inflation rate of 5.4%, we will use the formula for calculating the future price with inflation: \[ \text{Future Price} = \text{Current Price} \times (1 + \text{Inflation Rate}) \] Given: - Current Price in 2015: R335,730 - Predicted Inflation Rate: 5.4% Let's calculate the inflation rate for each year and then find the cost of a new VITO in 2016. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{321993}{307230}\right)-1\) - step1: Reduce the fraction: \(\frac{807}{770}-1\) - step2: Reduce fractions to a common denominator: \(\frac{807}{770}-\frac{770}{770}\) - step3: Transform the expression: \(\frac{807-770}{770}\) - step4: Subtract the numbers: \(\frac{37}{770}\) The inflation rate from 2013 to 2014 is approximately 0.0480519 or 4.80519%. Now, let's calculate the inflation rate from 2014 to 2015. Calculate the value by following steps: - step0: Calculate: \(\left(\frac{335730}{321993}\right)-1\) - step1: Reduce the fraction: \(\frac{5890}{5649}-1\) - step2: Reduce fractions to a common denominator: \(\frac{5890}{5649}-\frac{5649}{5649}\) - step3: Transform the expression: \(\frac{5890-5649}{5649}\) - step4: Subtract the numbers: \(\frac{241}{5649}\) The inflation rate from 2014 to 2015 is approximately 0.042662 or 4.2662%. Now, let's calculate the inflation rate from 2015 to 2016. Calculate the value by following steps: - step0: Calculate: \(\left(335730\times 1.054\right)-335730\) - step1: Multiply the numbers: \(353859.42-335730\) - step2: Subtract the numbers: \(18129.42\) The inflation rate from 2015 to 2016 is approximately 5.4%. Therefore, the year with the highest inflation rate is 2016 with an inflation rate of 5.4%. Now, let's calculate the cost of a new VITO in 2016. Calculate the value by following steps: - step0: Calculate: \(335730\times 1.054\) - step1: Multiply the numbers: \(353859.42\) The cost of a new VITO in 2016, considering the predicted inflation rate of 5.4%, would be approximately R353,859.42.