In the last presentation, I explained thoroughly what hire purchase is and we saw two worked examples to show how one can calculate some aspects of hire purchase such as the balance and total amount to be repaid. I decided to give further examples that demonstrates other components of hire purchase and how to calculate them. If you really missed the introductory part of this topic, feel free to check it out through this link.
So right now, we are going to see two more examples of hire purchase agreements where other aspects are required to be figured out through calculations.
Example 1: Under a hire purchase agreement, a buyer could purchase a piano if he makes an initial deposit of $2500 which is 25% of the total cost. He is expected to pay $500 per month for a period of 48 months. Calculate the following:
(i) The balance remaining after the initial deposit.
(iii) The total interest paid by the customer.
Solution:
Initial deposit = 2500
Monthly installment= 500
Time period= 48 months
Solving the first question: (i) The balance remaining after the initial deposit.
First we need to find the total cost of the Piano which 2500 represents 10% of it
Let Z represent the total cost, then we have
10/100 x Z =2500
0.1Z=2500
Z = 2500/0.1
Z = 25,000
Since the total cost of the Piano is $25,000, the we can easily find the balance by subtracting the initial deposit from the cost
The balance is: 25000 - 2500 = $22,500.
Next question is: (iii) The total interest paid by the customer.
To find the total interest, we need to find the total amount paid by the customer. That is the initial deposit and the installments. Then we can subtract the original cost from it. Therefore:
Total interest = Total amount paid - Original price
= (500x48) + 2500 - 25000
= 24000+2500-25000
= 26500-25000
=$1,500
Example 2: A smart phone is sold for an initial deposit of $1300 which is 1/4 of the original price. The customer has to pay $208 per month, and finish the balance within 1 year. Find the Original price of the television
Solution
Initial deposit = 1300
Repayment amount = 208
Period of repayment = 12 months
**to find the original price, we simply calculate for the number whose 1/4 is 1300.
Let the original price be p
Then, we have: 1/4 x p = 1300
0.25p = 1300
p = 1300/0.25
p = 5200
Therefore, the original price is $5200
Important tip to keep in mind
- Original price and hire purchase price: The original price and hire purchase price of any items are usually not the same. The seller makes profit for the lost time during repayment periods by adding some money or interest to the original price. Because of this, the hire purchase price is significantly higher than the original price of any goods. While the buyer utilizes the repayment time and installment style of to make a hire purchase of something they could not afford to pay at once, the seller makes profit through the interest added.
So in order to solve hire purchase arithmetic without much challenge, the student always need to find the difference between the hire purchase price and original cost of the item. Once this figure is well established, the rest is usually very easy to solve in all cases of hire purchase calculations.