Answer :
Sure, let's go through each part of the assignment step-by-step:
1.2 Mr Mokhethi invested R10 000 at another bank at an interest rate of 7.5% compounded annually. Determine the value of the investment after 2 years.
To find the value of an investment compounded annually, you can 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.
For this problem:
- [tex]\( P = 10000 \)[/tex]
- [tex]\( r = 7.5\% = 0.075 \)[/tex]
- [tex]\( n = 1 \)[/tex] (since it's compounded annually)
- [tex]\( t = 2 \)[/tex]
[tex]\[ A = 10000 \left(1 + \frac{0.075}{1}\right)^{1 \cdot 2} \][/tex]
[tex]\[ A = 10000 \left(1 + 0.075\right)^2 \][/tex]
[tex]\[ A = 10000 \left(1.075\right)^2 \][/tex]
[tex]\[ A = 10000 \times 1.15625 \][/tex]
[tex]\[ A = 11556.25 \][/tex]
Therefore, the value of Mr Mokhethi's investment after 2 years is R11,556.25.
1.3 Below is the list of groceries with the average prices for each item in 2022 and in 2023.
[tex]\[ \begin{array}{|l|c|c|c|} \hline \text{Item} & \text{Price 2022} & \text{Price 2023} & \% \text{ Change} \\ \hline \text{Bread (loaf)} & \text{R 17.00} & \text{R 19.50} & A \\ \hline \text{Milk (I)} & \text{R 16.49} & B & 14\% \\ \hline \text{Wild Island (juice)} & C & \text{R 16.99} & 5\% \\ \hline \text{Chicken (2kg)} & \text{R 55.00} & \text{R 72.50} & D \\ \hline \end{array} \][/tex]
1.3.1 Define the term inflation.
Inflation is the rate at which the general price level of goods and services rises, resulting in a decrease in the purchasing power of a currency.
1.3.2 Determine the price of milk in 2023 if the average inflation rate was 14%.
Given:
- Price of milk in 2022 was R16.49
- Inflation rate is 14%
[tex]\[ \text{Price in 2023} = \text{Price in 2022} \times (1 + \text{Inflation rate}) \][/tex]
[tex]\[ \text{Price in 2023} = 16.49 \times (1 + 0.14) \][/tex]
[tex]\[ \text{Price in 2023} = 16.49 \times 1.14 \][/tex]
[tex]\[ \text{Price in 2023} \approx 18.80 \][/tex]
So the price of milk in 2023 is approximately R18.80.
1.3.3 Calculate the percentage change of bread.
The percentage change is calculated as:
[tex]\[ \% \text{Change} = \left(\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}}\right) \times 100 \][/tex]
For bread:
- Old Price = R17.00
- New Price = R19.50
[tex]\[ \% \text{Change} = \left(\frac{19.50 - 17.00}{17.00}\right) \times 100 \][/tex]
[tex]\[ \% \text{Change} = \left(\frac{2.50}{17.00}\right) \times 100 \][/tex]
[tex]\[ \% \text{Change} \approx 14.71\% \][/tex]
So, the percentage change in the price of bread is approximately 14.71%.
1.3.4 Explain what it means if the inflation rate is 5.3%.
An inflation rate of 5.3% means that, on average, the prices of goods and services in the economy are rising by 5.3% over a year. This indicates that the purchasing power of the currency is decreasing, as you will need more money to buy the same goods and services than you did before.
1.3.5 Calculate the price of the juice (Wild Island) in 2022 if it has increased by 5%.
Given:
- Price of juice in 2023 is R16.99
- Inflation rate is 5%
To find the price in 2022, we need to reverse the inflation calculation:
[tex]\[ \text{Price in 2022} = \frac{\text{Price in 2023}}{1 + \text{Inflation rate}} \][/tex]
[tex]\[ \text{Price in 2022} = \frac{16.99}{1.05} \][/tex]
[tex]\[ \text{Price in 2022} \approx 16.18 \][/tex]
So, the price of the juice in 2022 was approximately R16.18.
1.2 Mr Mokhethi invested R10 000 at another bank at an interest rate of 7.5% compounded annually. Determine the value of the investment after 2 years.
To find the value of an investment compounded annually, you can 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.
For this problem:
- [tex]\( P = 10000 \)[/tex]
- [tex]\( r = 7.5\% = 0.075 \)[/tex]
- [tex]\( n = 1 \)[/tex] (since it's compounded annually)
- [tex]\( t = 2 \)[/tex]
[tex]\[ A = 10000 \left(1 + \frac{0.075}{1}\right)^{1 \cdot 2} \][/tex]
[tex]\[ A = 10000 \left(1 + 0.075\right)^2 \][/tex]
[tex]\[ A = 10000 \left(1.075\right)^2 \][/tex]
[tex]\[ A = 10000 \times 1.15625 \][/tex]
[tex]\[ A = 11556.25 \][/tex]
Therefore, the value of Mr Mokhethi's investment after 2 years is R11,556.25.
1.3 Below is the list of groceries with the average prices for each item in 2022 and in 2023.
[tex]\[ \begin{array}{|l|c|c|c|} \hline \text{Item} & \text{Price 2022} & \text{Price 2023} & \% \text{ Change} \\ \hline \text{Bread (loaf)} & \text{R 17.00} & \text{R 19.50} & A \\ \hline \text{Milk (I)} & \text{R 16.49} & B & 14\% \\ \hline \text{Wild Island (juice)} & C & \text{R 16.99} & 5\% \\ \hline \text{Chicken (2kg)} & \text{R 55.00} & \text{R 72.50} & D \\ \hline \end{array} \][/tex]
1.3.1 Define the term inflation.
Inflation is the rate at which the general price level of goods and services rises, resulting in a decrease in the purchasing power of a currency.
1.3.2 Determine the price of milk in 2023 if the average inflation rate was 14%.
Given:
- Price of milk in 2022 was R16.49
- Inflation rate is 14%
[tex]\[ \text{Price in 2023} = \text{Price in 2022} \times (1 + \text{Inflation rate}) \][/tex]
[tex]\[ \text{Price in 2023} = 16.49 \times (1 + 0.14) \][/tex]
[tex]\[ \text{Price in 2023} = 16.49 \times 1.14 \][/tex]
[tex]\[ \text{Price in 2023} \approx 18.80 \][/tex]
So the price of milk in 2023 is approximately R18.80.
1.3.3 Calculate the percentage change of bread.
The percentage change is calculated as:
[tex]\[ \% \text{Change} = \left(\frac{\text{New Price} - \text{Old Price}}{\text{Old Price}}\right) \times 100 \][/tex]
For bread:
- Old Price = R17.00
- New Price = R19.50
[tex]\[ \% \text{Change} = \left(\frac{19.50 - 17.00}{17.00}\right) \times 100 \][/tex]
[tex]\[ \% \text{Change} = \left(\frac{2.50}{17.00}\right) \times 100 \][/tex]
[tex]\[ \% \text{Change} \approx 14.71\% \][/tex]
So, the percentage change in the price of bread is approximately 14.71%.
1.3.4 Explain what it means if the inflation rate is 5.3%.
An inflation rate of 5.3% means that, on average, the prices of goods and services in the economy are rising by 5.3% over a year. This indicates that the purchasing power of the currency is decreasing, as you will need more money to buy the same goods and services than you did before.
1.3.5 Calculate the price of the juice (Wild Island) in 2022 if it has increased by 5%.
Given:
- Price of juice in 2023 is R16.99
- Inflation rate is 5%
To find the price in 2022, we need to reverse the inflation calculation:
[tex]\[ \text{Price in 2022} = \frac{\text{Price in 2023}}{1 + \text{Inflation rate}} \][/tex]
[tex]\[ \text{Price in 2022} = \frac{16.99}{1.05} \][/tex]
[tex]\[ \text{Price in 2022} \approx 16.18 \][/tex]
So, the price of the juice in 2022 was approximately R16.18.
