SOLUTION: The hire purchase price of a refrigerator is 6000. The deposit of 500 is made and the remainder is paid in equal monthly payments of 2500. a) if the cash price is 4000, express

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Question 1178048: The hire purchase price of a refrigerator is 6000. The deposit of 500 is made and the remainder is paid in equal monthly payments of 2500.
a) if the cash price is 4000, express as a percentage of the cash price, the extra cost of buying on hire purchase.
b) what is the interest rate (simple interest) charged on this transaction
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve this problem step-by-step.
**a) Extra Cost of Hire Purchase**
1. **Calculate the Total Amount Paid in Installments:**
* Hire purchase price: 6000
* Deposit: 500
* Amount paid in installments: 6000 - 500 = 5500
2. **Calculate the Extra Cost:**
* Cash price: 4000
* Total amount paid on hire purchase: 500 (deposit) + 5500 (installments) = 6000
* Extra cost: 6000 - 4000 = 2000
3. **Express as a Percentage of the Cash Price:**
* Percentage extra cost = (Extra cost / Cash price) * 100
* Percentage extra cost = (2000 / 4000) * 100 = 0.5 * 100 = 50%
**Therefore, the extra cost of buying on hire purchase is 50% of the cash price.**
**b) Interest Rate (Simple Interest)**
1. **Calculate the Total Interest Paid:**
* Total interest = 2000 (from part a)
2. **Determine the Number of Installments:**
* Amount paid in installments: 5500
* Monthly payment: 2500
* Number of installments: 5500 / 2500 = 2.2. This indicates that there are two full payments and a partial payment. Therefore there are 3 payments.
3. **Calculate the Time Period:**
* Since there are 3 payments, the time period is 3 months.
4. **Calculate the Principal:**
* The principal is the cash price minus the deposit: 4000 - 500 = 3500
5. **Use the Simple Interest Formula:**
* Simple Interest (I) = Principal (P) * Rate (R) * Time (T)
* 2000 = 3500 * R * (3/12) (Time is in years, so 3 months = 3/12 years)
* 2000 = 3500 * R * 0.25
* 2000 = 875 * R
* R = 2000 / 875 ≈ 2.2857
6. **Convert to Percentage:**
* R ≈ 2.2857 * 100 = 228.57% per year
**Therefore, the simple interest rate charged on this transaction is approximately 228.57% per year.**