\begin{tabular}{l} 4.5 You borrow R6 500 for 3 years, on the condition that you pay it back with \ $$ 15 \% $$ p.a. simple interest. How much interest will you have to pay back on \ this loan? \ $$ 4.6 \begin{array}{l} ext { Saleh buys a car costing R120 000 on hire purchase. He makes a R10 000 } \ ext { deposit and pays back the balance, with 14\% p.a. simple interest, over a } \ ext { period of } 60 ext { months. Calculate his monthly payment. }\end{array} $$ \ \hline\end{tabular}

Question

\begin{tabular}{l} 4.5 You borrow R6 500 for 3 years, on the condition that you pay it back with \ $$ 15 \% $$ p.a. simple interest. How much interest will you have to pay back on \ this loan? \ $$ 4.6 \begin{array}{l}	ext { Saleh buys a car costing R120 000 on hire purchase. He makes a R10 000 } \ 	ext { deposit and pays back the balance, with 14\% p.a. simple interest, over a } \ 	ext { period of } 60 	ext { months. Calculate his monthly payment. }\end{array} $$ \ \hline\end{tabular}

UpStudy AI · Accepted Answer

**4.5 Calculation of Interest on a R6 500 Loan**

1. For simple interest, the formula is  
   $$
   \text{Interest} = P \times r \times t,
   $$  
   where:  
   - $$ P = 6500 $$ (principal),  
   - $$ r = 0.15 $$ (annual interest rate),  
   - $$ t = 3 $$ years.

2. Substitute the values into the formula:  
   $$
   \text{Interest} = 6500 \times 0.15 \times 3.
   $$

3. Calculate step by step:  
   $$
   6500 \times 0.15 = 975,
   $$  
   then,  
   $$
   975 \times 3 = 2925.
   $$

4. Therefore, the interest to be paid is  
   $$
   R2925.
   $$

---

**4.6 Calculation of Saleh's Monthly Payment on a Car**

1. **Determine the balance to be financed:**  
   The cost of the car is $$ R120\,000 $$ and Saleh makes a deposit of $$ R10\,000 $$.  
   $$
   \text{Principal} = 120\,000 - 10\,000 = R110\,000.
   $$

2. **Calculate the total interest using simple interest:**  
   The annual interest rate is $$ 0.14 $$ and the loan period is 60 months (or 5 years).  
   $$
   \text{Interest} = P \times r \times t = 110\,000 \times 0.14 \times 5.
   $$

3. Compute the interest:  
   $$
   110\,000 \times 0.14 = 15\,400,
   $$  
   then,  
   $$
   15\,400 \times 5 = 77\,000.
   $$

4. **Determine the total amount to be repaid:**  
   $$
   \text{Total amount} = \text{Principal} + \text{Interest} = 110\,000 + 77\,000 = R187\,000.
   $$

5. **Calculate the monthly payment:**  
   The repayment period is 60 months, so:  
   $$
   \text{Monthly payment} = \frac{187\,000}{60} \approx R3116.67.
   $$

6. Therefore, Saleh’s monthly payment is approximately  
   $$
   R3116.67.
   $$
**4.5 Interest Calculation** - Borrowed amount: R6,500 - Interest rate: 15% per annum - Time: 3 years Interest = 6,500 × 0.15 × 3 = R2,925 **4.6 Saleh's Monthly Payment** - Car cost: R120,000 - Deposit: R10,000 - Principal: R110,000 - Interest rate: 14% per annum - Loan period: 60 months (5 years) Total interest = 110,000 × 0.14 × 5 = R77,000 Total repayment = 110,000 + 77,000 = R187,000 Monthly payment = 187,000 ÷ 60 ≈ R3,116.67

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