Sure, let's break down the problem step-by-step.
### Given Information:
- Principal amount (initial investment): R12,000
- Time period: 5 years
- Simple interest rate per annum: 10%
### Solution:
#### 1.1.1 Identify the interest rate for the investment.
The interest rate for the investment is clearly stated as 10% per annum.
#### 1.1.2 How much will Miss Matsheka have in total after 5 years?
To find out the total amount that Miss Matsheka will have after 5 years, we need to first calculate the simple interest she will earn over this period and then add it to her principal amount.
Step 1: Calculate the Simple Interest
Simple Interest can be calculated using the formula:
[tex]\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Where:
- Principal (P) = R12,000
- Rate (R) = 10% per annum = 0.10 (as a decimal)
- Time (T) = 5 years
Using the formula,
[tex]\[ \text{Simple Interest} = 12,000 \times 0.10 \times 5 \][/tex]
[tex]\[ \text{Simple Interest} = 12,000 \times 0.50 \][/tex]
[tex]\[ \text{Simple Interest} = 6,000 \][/tex]
So, Miss Matsheka will earn R6,000 in interest over 5 years.
Step 2: Calculate the Total Amount after 5 years
The total amount after 5 years can be found by adding the interest earned to the principal amount.
[tex]\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \][/tex]
Using the values,
[tex]\[ \text{Total Amount} = 12,000 + 6,000 \][/tex]
[tex]\[ \text{Total Amount} = 18,000 \][/tex]
Therefore, Miss Matsheka will have R18,000 in total after 5 years.
