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Activity 3: Individual Work

3.1 Use the prices in 2.1 of Activity 2 to determine your second choice of car rental if your first choice as a group is no longer available and calculate:

a) The extra money you will require for your second option if the amount of money you have fundraised as a class is R 1,200 less than the total amount for the material/equipment, excluding the car hire.
(2)
[tex]\[ R 5,684.40 + R 3,469.96 = R 9,154.36 \][/tex]
[tex]\[ R 9,154.36 - R 4,484.40 = R 4,669.96 \][/tex]

Amount fundraised:
[tex]\[ \text{Amount fundraised} \][/tex]
[tex]\[ R 5,684.40 - 1,200 = R 4,484.40 \][/tex]

b) Simple interest on the amount in 3.1(a) above at a rate of 12% per annum over 2 years if your class teacher offers to get a loan on your behalf.
(3)



Answer :

GinnyAnswer
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.