3. Mr Hassiem buys a computer for his business on hire purchase. The price of the computer is R8 999 and he pays a deposit of R1 500 . The simple Interest rate is 7\% p.a. Calculate his monthly instalment if the hire purchas agreement says that he must pay back the money in 3 years' time. 4. Abusiswe loans R78 500 from a bank to buy a car. She agrees to repay the amount with interest in equal monthly instalments. The bank adds simple interest at a rate of $$ 7,5 \% $$ over 3 years to the amount. Calculate the followir 4.1 the total amount Abusiswe has to pay

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Let's solve each problem step by step.

### Problem 3: Mr. Hassiem's Computer Hire Purchase

**Known Conditions:**
- Price of the computer: $$ P = 8999 $$
- Deposit paid: $$ D = 1500 $$
- Simple interest rate: $$ r = 7\% $$ per annum
- Time period: $$ t = 3 $$ years

**Step 1: Calculate the amount financed.**
The amount financed is the price of the computer minus the deposit:
$$
A = P - D = 8999 - 1500 = 7499
$$

**Step 2: Calculate the total interest over 3 years.**
Using the formula for simple interest:
$$
I = A \cdot r \cdot t
$$
where $$ r $$ is in decimal form:
$$
r = \frac{7}{100} = 0.07
$$
Now, substituting the values:
$$
I = 7499 \cdot 0.07 \cdot 3
$$

**Step 3: Calculate the total amount to be paid back.**
The total amount to be paid back is the amount financed plus the interest:
$$
T = A + I
$$

**Step 4: Calculate the monthly instalment.**
The total number of months over 3 years is:
$$
n = 3 \cdot 12 = 36
$$
The monthly instalment $$ M $$ is given by:
$$
M = \frac{T}{n}
$$

Now, let's perform the calculations.

### Problem 4: Abusiswe's Car Loan

**Known Conditions:**
- Loan amount: $$ L = 78500 $$
- Simple interest rate: $$ r = 7.5\% $$ per annum
- Time period: $$ t = 3 $$ years

**Step 1: Calculate the total interest over 3 years.**
Using the formula for simple interest:
$$
I = L \cdot r \cdot t
$$
where $$ r $$ is in decimal form:
$$
r = \frac{7.5}{100} = 0.075
$$
Now, substituting the values:
$$
I = 78500 \cdot 0.075 \cdot 3
$$

**Step 2: Calculate the total amount to be paid back.**
The total amount to be paid back is the loan amount plus the interest:
$$
T = L + I
$$

Now, let's perform the calculations for both problems.
Calculate the value by following steps:
- step0: Calculate:
  $$7499\times 0.07\times 3$$
- step1: Multiply the terms:
  $$524.93\times 3$$
- step2: Multiply the numbers:
  $$1574.79$$
Calculate or simplify the expression $$ 78500 * 0.075 * 3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$78500\times 0.075\times 3$$
- step1: Multiply the terms:
  $$5887.5\times 3$$
- step2: Multiply the numbers:
  $$17662.5$$
Calculate or simplify the expression $$ 78500 + 17662.5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$78500+17662.5$$
- step1: Add the numbers:
  $$96162.5$$
Calculate or simplify the expression $$ 7499 + 1574.79 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7499+1574.79$$
- step1: Add the numbers:
  $$9073.79$$
Calculate or simplify the expression $$ 9073.79 / 36 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{9073.79}{36}$$
- step1: Convert the expressions:
  $$\frac{\frac{907379}{100}}{36}$$
- step2: Multiply by the reciprocal:
  $$\frac{907379}{100}\times \frac{1}{36}$$
- step3: Multiply the fractions:
  $$\frac{907379}{100\times 36}$$
- step4: Multiply:
  $$\frac{907379}{3600}$$
Calculate or simplify the expression $$ 96162.5 / (3 * 12) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{96162.5}{\left(3\times 12\right)}$$
- step1: Remove the parentheses:
  $$\frac{96162.5}{3\times 12}$$
- step2: Multiply the numbers:
  $$\frac{96162.5}{36}$$
- step3: Convert the expressions:
  $$\frac{\frac{192325}{2}}{36}$$
- step4: Multiply by the reciprocal:
  $$\frac{192325}{2}\times \frac{1}{36}$$
- step5: Multiply the fractions:
  $$\frac{192325}{2\times 36}$$
- step6: Multiply:
  $$\frac{192325}{72}$$
### Solution to Problem 3: Mr. Hassiem's Computer Hire Purchase

1. **Amount Financed:**
   $$
   A = 8999 - 1500 = 7499
   $$

2. **Total Interest Calculation:**
   $$
   I = 7499 \cdot 0.07 \cdot 3 = 1574.79
   $$

3. **Total Amount to be Paid Back:**
   $$
   T = 7499 + 1574.79 = 9073.79
   $$

4. **Monthly Instalment Calculation:**
   $$
   n = 3 \cdot 12 = 36
   $$
   $$
   M = \frac{9073.79}{36} \approx 252.05
   $$

**Final Answer for Problem 3:**
Mr. Hassiem's monthly instalment is approximately **R252.05**.

---

### Solution to Problem 4: Abusiswe's Car Loan

1. **Total Interest Calculation:**
   $$
   I = 78500 \cdot 0.075 \cdot 3 = 17662.5
   $$

2. **Total Amount to be Paid Back:**
   $$
   T = 78500 + 17662.5 = 96162.5
   $$

3. **Monthly Instalment Calculation:**
   $$
   n = 3 \cdot 12 = 36
   $$
   $$
   M = \frac{96162.5}{36} \approx 2671.18
   $$

**Final Answer for Problem 4:**
The total amount Abusiswe has to pay is **R96,162.50**.
**Problem 3:** - **Monthly Instalment:** R252.05 **Problem 4:** - **Total Amount to Pay:** R96,162.50

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