Dear Secondary Math students, we will be covering the topic on Hire Purchase today. This is an extremely useful topic as we will be using most of the concepts learnt in our day to day lives. Without further ado, let's begin!

__How to apply concepts of simple interest in questions involving hire purchases__

After learning about ** simple and compound interest** in the previous article (and if you haven’t, do check it out on the link!), we will be learning about the application of simple interest in the real-life world context, and one very good and relevant example would be hire purchases.

Hire purchase is defined to be a system which after a purchase is made, the buyer has to firstly pay a specific amount agreed by the buyer and seller (down payment), followed by paying a mutually agreed amount on regular periods (instalments), which is also decided mutually between the buyer and seller, with an additional interest based on the periods.

Let us try an example to give you a better understanding on this question type:

**Mr Lim wants to purchase a 42-inch television for a retail cost of $6500. Mr Lim decided to purchase the television on hire purchase. The store requires Mr Lim to place a down payment of $1500, and charges a simple interest of 3.5% per annum for the monthly instalments of $250. How much will Mr Lim have to pay in total to clear off his debts?**

First, let’s break down the question. The retail cost of the television is $6500, which means that it is the initial principal amount to be paid without interest, a down payment of $1500 is to be paid with a monthly instalment of $250 with an additional simple interest of 3.5%. The general formula we will be using here is:

**Total amount to be paid = Initial down payment + monthly instalments with interest**

Let’s recap on the topic of simple interest. We know that the formulae for simple interest is:

**I = (PRT)/100**

**where I = total interest, P = the initial or principal amount, R = interest rate, T = number of time period (in years) **

Now, to begin, we must deduct off the initial down payment from the retail cost of the television, because it has already been paid by Mr Lim, hence it should not be accounted in any of the simple interest charged.

**$6500 (Retail cost) - $1500 (Down payment) = $5000**

The remaining $5000 will be the amount left that is subjected to the simple interest rate charges. If we apply the formula of simple interest, it will look something like this:

**I = PRT/100**

**I = (5000) (3.5) T/100**

If you realize, we do not have the value of T. So, what should we do? We can simply divide the principal amount by the amount to be paid in a month, omitting the portion which includes the interest rate charges. Therefore,

**$5000 / $250 = 20 months**

**20 months converted into years would be 20 / 12 = 5/3**

Now let’s just pluck in the value of T back into the formula!

**I = PRT/100**

**I = (5000) (3.5) (5/3)/100**

**I = $291.666667 **

**~ $291.67 (2 d.p)**

**Therefore, since total amount to be paid = initial down payment + monthly instalments with interest,**

**Total amount to be paid = $1500 + $5000 + $291.67**

**= $6791.67 **

__Question time!__

1. Jack purchased a computer using a payment plan offered by the store. The conditions were stated,” Cash Price = $2300, or 20% down payment plus 12 equal payments of $160 each”. Hence, calculate

a) the deposit

b) the total monthly payments

c) the total cost of the computer on the payment plan

d) how much would she have saved by paying cash in full 2. John wants to buy a new Nintendo Switch Console. It costs $700 but John is unable to pay in full since he is still a student. Hence, he decides to pay based on monthly instalment. The store requires him to pay an initial down payment of $100, and a monthly instalment of $50. If John paid a total of $724 to clear off his debts, how much did the bank charge for the interest rate per annum?

3. The price of a new-model speakers cost $3500. Tim bought the speakers on hire purchase by placing a down payment of $500, and is required to pay a monthly instalment of $150 over x months.

a) Express the total amount payable by hire purchase, in terms of x

b) Express, in terms of x, the amount Mr Tan could have saved if he had paid in full by cash

c) Given that the seller charged simple interest rate at 10% per annum, form an equation to calculate the value of x

And that’s all we have for today, students! ** Math Lobby** hopes that after this article, all of you would have a good understanding of how the concepts of simple interest can be applied in the real-world context! If you have any questions or queries, please feel free to contact Math Lobby on our Facebook page, Instagram or on the Math Lobby website itself!

As always: Work hard, stay motivated and we wish all students a successful and enjoyable journey with Math Lobby!

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