Question

Abhinav purchases a track suit for Rs. 2400 cash or for Rs. 1000 cash down payments and two monthly instaiments of Rs. 800 each. Find the rate of interest: (a) \(75 \%\) (b) \(120 \%\) (c) \(50 \%\) (d) none of these

Short answer

Answer: 50%

Step-by-step solution

Calculate the amount paid by Abhinav using the installment method

Abhinav buys the track suit by paying Rs. 1000 cash down and follows up with two monthly installments of Rs. 800 each. To determine the total amount paid through this method, we need to sum up the initial down payment and the two monthly installments. The total amount paid can be calculated as follows: Total amount = Initial down payment + (Monthly installment × 2)

Calculate Total Amount Paid

Now, let's determine the total amount Abhinav paid using the installment method: Total amount = 1000 + (800 × 2) Total amount = 1000 + 1600 Total amount = Rs. 2600

Calculate the Difference between the cash price and the total amount paid using the installment method

Next, let's find out how much extra Abhinav paid using the installment method compared to the original cash price: Extra amount paid = Total amount paid (installment method) – Cash price Extra amount paid = 2600 – 2400 Extra amount paid = Rs. 200

Calculate the Rate of Interest

To determine the rate of interest charged for the extra payment made using the installment method, we need to find out the interest percentage for the first installment, which is the extra amount paid (Rs. 200) out of Rs. 800 (the first installment): Rate of interest = (Extra amount paid / First installment) * 100 Rate of interest = (200 / 800) * 100 Rate of interest = 0.25 * 100 Rate of interest = 25% Now, since 25% interest is charged only for the first installment, for the total price (Rs. 2000) of the track suit, the rate of interest will be 50%. Thus, the correct option is: (c) \(50 \%\)

Key concepts

Installment Payments

When you buy an item on installment, you agree to pay a fixed initial amount, called a down payment, followed by a series of periodic payments until the item's total cost is paid off. This is a common method used by merchants to make an item more affordable in the short term while allowing the buyer to use it immediately.

For example, Abhinav decided to buy a track suit using the installment method by making a down payment of Rs. 1000, followed by two monthly installments of Rs. 800 each. The key consideration when opting for installments is the total cost at the end of the payment period, which includes the rate of interest applied to the installment amount. By comparing this total to the cash price, one can determine the additional cost incurred due to the convenience of installment payments.

Cost Comparison

Cost comparison is essential when evaluating payment options, as it helps you understand how different methods affect the ultimate price. When comparing the installment cost to the one-time cash price, consider the total payment made over the installment period versus the upfront cash payment.

In our case, Abhinav would pay Rs. 2400 if he chose the cash option, but he ends up paying Rs. 2600 by choosing installments. By comparing these costs, Abhinav can see that he is paying an extra Rs. 200 when opting to buy the tracksuit with installments. This cost comparison reveals the additional financial burden created by installment payments, which is often due to the interest rate applied to the deferred payments.

Percentage Calculation

Percentage calculation is a mathematical concept used to compare relative values or to find out what portion one quantity is of another. It's commonly represented by the '%' symbol and is an important part of understanding financial terms like interest rates.

For Abhinav's installment plan, the extra amount paid beyond the cash price reflects the interest. To calculate the rate of interest as a percentage, we take the extra amount paid (Rs. 200) over the cost of the first installment post down payment (Rs. 800). Through percentage calculation formula, \( \text{Rate of interest} = \frac{\text{Extra amount paid}}{\text{First installment}} \times 100 \), we found that the rate of interest for the installment amounted to 25% for the first month. By doubling that because there are two installments, we determine an overall interest rate of 50% on the financed amount.

Quantitative Aptitude

Quantitative aptitude involves the ability to solve numerical and logical problems. It's a skill that comes in handy when dealing with exercises that involve numbers, like interest calculations and installment payments.

In solving our textbook problem, a strong quantitative aptitude allowed us to identify the steps needed: calculate the total installment payment, determine the excess payment over the cash price, and then calculate the interest rate as a percentage. Mastering quantitative aptitude not only helps to solve such textbook problems but also builds a foundation for making informed financial decisions in real life. It's a critical skill for students because it is widely applicable, from everyday life calculations to complex financial analyses.