The hire purchase price of a refrigerator is R6 500 . The deposit of R500 is made and
the remainder is paid in equal monthly payments of R250.
a. Calculate the number of monthly payments that must be made.
What is the interest rate (simple interest) charged on this transaction?
cost of buying on hire purchase.

Question

UpStudy AI · Accepted Answer

**Step 1. Calculate the amount to be financed**

The total hire purchase price is  
$$
6500.
$$  
A deposit of  
$$
500
$$  
is paid upfront. Therefore, the remainder to be paid is  
$$
6500 - 500 = 6000.
$$

---

**Step 2. Determine the number of monthly payments**

The remainder of  
$$
6000
$$  
is paid in equal monthly payments of  
$$
250.
$$  
Thus, the number of monthly payments is calculated as  
$$
\frac{6000}{250} = 24.
$$

---

**Step 3. Establish the total cost and interest amount**

Since the total amount paid in hire purchase is  
$$
6500,
$$  
if we assume that the non-hire-purchase (cash) price would be the amount financed (i.e.  
$$
6000
$$  
for the balance), then the extra cost (or interest) charged for using hire purchase is  
$$
6500 - 6000 = 500.
$$

---

**Step 4. Calculate the simple interest rate**

The interest is charged on the amount financed, which is  
$$
6000.
$$  
The total interest over the period (from the additional cost) is  
$$
500.
$$

The repayment term is 24 months, which is equivalent to  
$$
\frac{24}{12} = 2 \text{ years}.
$$

Let the simple interest rate per annum be $$ r $$ (in decimal form). According to the simple interest formula,  
$$
I = P \times r \times t,
$$
where  
$$
I = 500,\quad P = 6000,\quad t = 2.
$$  
Substitute the values into the formula:  
$$
500 = 6000 \times r \times 2.
$$

Solve for $$ r $$:

$$
500 = 12000 \, r \quad \Longrightarrow \quad r = \frac{500}{12000} = \frac{1}{24} \approx 0.04167.
$$

Converting to a percentage:

$$
0.04167 \times 100 \approx 4.17\% \text{ per annum}.
$$

---

**Summary of Answers**

- Number of monthly payments:  
  $$
  24.
  $$

- Interest rate (simple interest) charged:  
  $$
  \approx 4.17\% \text{ per annum}.
  $$
- **Number of Monthly Payments:** 24 - **Interest Rate (Simple Interest):** Approximately 4.17% per annum

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