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

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) (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.**

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