Answer :
Let's tackle each part of the assignment step-by-step.
### 1.2 Mr. Mokhethi's Investment
Mr. Mokhethi invested R10,000 at an interest rate of 7.5% compounded annually. To find the value of the investment after 2 years, we use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the time the money is invested for in years.
In this case:
- [tex]\( P = 10,000 \)[/tex]
- [tex]\( r = 7.5\% = 0.075 \)[/tex]
- [tex]\( n = 1 \)[/tex] (compounded annually)
- [tex]\( t = 2 \)[/tex] years
Plug these values into the formula:
[tex]\[ A = 10,000 \left(1 + \frac{0.075}{1}\right)^{1 \cdot 2} \][/tex]
[tex]\[ A = 10,000 \left(1 + 0.075\right)^2 \][/tex]
[tex]\[ A = 10,000 \left(1.075\right)^2 \][/tex]
[tex]\[ A = 10,000 \left(1.155625\right) \][/tex]
[tex]\[ A = 11,556.25 \][/tex]
So, the value of the investment after 2 years is R11,556.25.
### 1.3.1 Definition of Inflation
Inflation is the rate at which the general level of prices for goods and services is rising and subsequently eroding the purchasing power of currency. It indicates how much more expensive a set of goods and services has become over a certain period, usually a year.
### 1.3.2 Price of Milk in 2023
Given that the price of milk in 2022 was R16.49 and the average inflation rate was 14%, we calculate the price in 2023 using the formula for calculating price increase due to inflation:
[tex]\[ \text{New Price} = \text{Old Price} \times (1 + \text{Inflation Rate}) \][/tex]
Here:
- Old Price = 16.49
- Inflation Rate = 14% = 0.14
[tex]\[ \text{New Price} = 16.49 \times (1 + 0.14) \][/tex]
[tex]\[ \text{New Price} = 16.49 \times 1.14 \][/tex]
[tex]\[ \text{New Price} = 18.8 \][/tex]
Thus, the price of milk in 2023 is R18.80.
### 1.3.3 Percentage Change of Bread
To calculate the percentage change in the price of bread from 2022 to 2023, use the formula for percentage change:
[tex]\[ \text{Percentage Change} = \left(\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}}\right) \times 100 \% \][/tex]
Here:
- Old Price = 17.00
- New Price = 19.50
[tex]\[ \text{Percentage Change} = \left(\frac{19.50 - 17.00}{17.00}\right) \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = \left(\frac{2.50}{17.00}\right) \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = 0.1470588235 \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = 14.71 \% \][/tex]
Thus, the percentage change in the price of bread is approximately 14.71%.
### 1.3.4 Explanation of 5.3% Inflation Rate
An inflation rate of 5.3% means that, on average, prices for goods and services have increased by 5.3% over a specified period, usually one year. This implies that items that may have cost 100 currency units in the previous year would now cost 105.3 currency units.
### 1.3.5 Price of Wild Island Juice in 2022
Given that the price of Wild Island juice in 2023 is R16.99 and it increased by 5%, we calculate the 2022 price using the formula:
[tex]\[ \text{Old Price} = \frac{\text{New Price}}{1 + \text{Inflation Rate}} \][/tex]
Here:
- New Price = 16.99
- Inflation Rate = 5% = 0.05
[tex]\[ \text{Old Price} = \frac{16.99}{1 + 0.05} \][/tex]
[tex]\[ \text{Old Price} = \frac{16.99}{1.05} \][/tex]
[tex]\[ \text{Old Price} = 16.18 \][/tex]
Thus, the price of Wild Island juice in 2022 was approximately R16.18.
### 1.2 Mr. Mokhethi's Investment
Mr. Mokhethi invested R10,000 at an interest rate of 7.5% compounded annually. To find the value of the investment after 2 years, we use the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (decimal).
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the time the money is invested for in years.
In this case:
- [tex]\( P = 10,000 \)[/tex]
- [tex]\( r = 7.5\% = 0.075 \)[/tex]
- [tex]\( n = 1 \)[/tex] (compounded annually)
- [tex]\( t = 2 \)[/tex] years
Plug these values into the formula:
[tex]\[ A = 10,000 \left(1 + \frac{0.075}{1}\right)^{1 \cdot 2} \][/tex]
[tex]\[ A = 10,000 \left(1 + 0.075\right)^2 \][/tex]
[tex]\[ A = 10,000 \left(1.075\right)^2 \][/tex]
[tex]\[ A = 10,000 \left(1.155625\right) \][/tex]
[tex]\[ A = 11,556.25 \][/tex]
So, the value of the investment after 2 years is R11,556.25.
### 1.3.1 Definition of Inflation
Inflation is the rate at which the general level of prices for goods and services is rising and subsequently eroding the purchasing power of currency. It indicates how much more expensive a set of goods and services has become over a certain period, usually a year.
### 1.3.2 Price of Milk in 2023
Given that the price of milk in 2022 was R16.49 and the average inflation rate was 14%, we calculate the price in 2023 using the formula for calculating price increase due to inflation:
[tex]\[ \text{New Price} = \text{Old Price} \times (1 + \text{Inflation Rate}) \][/tex]
Here:
- Old Price = 16.49
- Inflation Rate = 14% = 0.14
[tex]\[ \text{New Price} = 16.49 \times (1 + 0.14) \][/tex]
[tex]\[ \text{New Price} = 16.49 \times 1.14 \][/tex]
[tex]\[ \text{New Price} = 18.8 \][/tex]
Thus, the price of milk in 2023 is R18.80.
### 1.3.3 Percentage Change of Bread
To calculate the percentage change in the price of bread from 2022 to 2023, use the formula for percentage change:
[tex]\[ \text{Percentage Change} = \left(\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}}\right) \times 100 \% \][/tex]
Here:
- Old Price = 17.00
- New Price = 19.50
[tex]\[ \text{Percentage Change} = \left(\frac{19.50 - 17.00}{17.00}\right) \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = \left(\frac{2.50}{17.00}\right) \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = 0.1470588235 \times 100 \% \][/tex]
[tex]\[ \text{Percentage Change} = 14.71 \% \][/tex]
Thus, the percentage change in the price of bread is approximately 14.71%.
### 1.3.4 Explanation of 5.3% Inflation Rate
An inflation rate of 5.3% means that, on average, prices for goods and services have increased by 5.3% over a specified period, usually one year. This implies that items that may have cost 100 currency units in the previous year would now cost 105.3 currency units.
### 1.3.5 Price of Wild Island Juice in 2022
Given that the price of Wild Island juice in 2023 is R16.99 and it increased by 5%, we calculate the 2022 price using the formula:
[tex]\[ \text{Old Price} = \frac{\text{New Price}}{1 + \text{Inflation Rate}} \][/tex]
Here:
- New Price = 16.99
- Inflation Rate = 5% = 0.05
[tex]\[ \text{Old Price} = \frac{16.99}{1 + 0.05} \][/tex]
[tex]\[ \text{Old Price} = \frac{16.99}{1.05} \][/tex]
[tex]\[ \text{Old Price} = 16.18 \][/tex]
Thus, the price of Wild Island juice in 2022 was approximately R16.18.
