(b) Mr Tan intends to buy the car using hire purchase. He has to make a
downpayment and pay monthly instalments of over 4 years.
Find the annual simple interest rate of this hire purchase scheme.

To solve this, let’s first calculate the total cost of the car. Since Mr. Tan needs to make a 20% downpayment, he will finance 80% of the car’s value through hire purchase.

Let’s denote the total car price as . The downpayment will be and the financed amount will be .

The total duration of the hire purchase scheme is 4 years, which corresponds to 48 monthly payments of $3200 each. So the total amount paid through installments is .

This indicates that the financed amount plus interest amounts to $153,600. Hence, we can express it as:

Where is the total interest paid over the course of the hire purchase.

The principal amount financed is which we can find from:

To calculate the total interest , we first need to determine the principal amount financed. Let’s calculate the downpayment and financed amount with some algebraic adjustments:

Now, the total amount paid is calculated as follows:
If the downpayment is 20%, then Mr. Tan is financing 80%, or:

Finally, the total interest paid is simply calculated as:

To find the original price , we use:

Where is the time period in years.

This will give you the desired annual interest rate once you find the financed amount or the original cost . You can substitute a number for to solve for the monthly payments and find . Happy calculating!