Let's work through the problem step by step.
### Part (a)
Step 1: Calculate the total cost of material/equipment.
The sum of R 5684.40 and R 3469.96 gives you the total material/equipment cost:
[tex]\[
5684.40 + 3469.96 = 9154.36
\][/tex]
Step 2: Determine the car hire cost and the amount fundraised.
The car hire cost is R 4484.40.
Your class has fundraised R 1200 less than this car hire cost. So, the amount fundraised is:
[tex]\[
4484.40 - 1200 = 3284.40
\][/tex]
Step 3: Calculate the extra money required for your second option.
The extra money required is the difference between the total material/equipment cost and the car hire cost:
[tex]\[
9154.36 - 4484.40 = 4669.96
\][/tex]
### Part (b)
Step 4: Calculate the simple interest on the extra money required.
The simple interest formula is: [tex]\( \text{Simple Interest} = P \times r \times t \)[/tex]
Where:
- [tex]\( P \)[/tex] is the principal amount (extra money required) = 4669.96
- [tex]\( r \)[/tex] is the interest rate per year = 12% or 0.12
- [tex]\( t \)[/tex] is the time in years = 2
Substituting these values in, we get:
[tex]\[
\text{Simple Interest} = 4669.96 \times 0.12 \times 2 = 1120.79
\][/tex]
Step 5: Calculate the total amount to be paid if the loan is taken.
The total amount with interest is the sum of the extra money required and the simple interest:
[tex]\[
4669.96 + 1120.79 = 5790.75
\][/tex]
### Summary of the Results
- The total material/equipment cost is R 9154.36.
- The amount fundraised is R 3284.40.
- The extra money required for your second option is R 4669.96.
- The simple interest over 2 years at a rate of 12% per annum is R 1120.79.
- The total amount to be paid if a loan is taken is R 5790.75.
