Question

A cellphone is available for Rs. 600 or for 300 cash down payment together with Rs. 360 to be paid after two months. Find the rate of interest charged under this scheme: (a) \(20 \%\) (b) \(50 \%\) (c) \(120 \%\) (d) none of these

Short answer

(a) 100% (b) 110% (c) 120% (d) 130% Answer: (c) 120%

Step-by-step solution

Analyze the given information

We have the outright price of the cellphone as Rs. 600. The other payment option involves a down payment of Rs. 300 and a payment of Rs. 360 after two months. We'll use this information to calculate the interest rate charged on the delayed payment.

Calculate the principal amount

The principal amount is the down payment made, which is Rs. 300. This is the amount on which interest will be calculated.

Calculate the interest amount

The interest amount is the difference between the outright price (Rs. 600) and the total amount paid in the second payment option (Rs. 660). So, the interest amount is: Interest = 660 - 600 = Rs. 60

Calculate the time period in years

The interest is charged for a period of 2 months. To calculate the rate of interest, we need the time period in years. Therefore, we'll convert the 2 months into years: Time = 2 months ÷ 12 months = \(\frac{1}{6}\) years

Use the simple interest formula to calculate the rate of interest

The simple interest formula is given as follows: Simple Interest = \(\frac{Principal \times Rate \times Time}{100}\) We need to find the rate (R). So, we'll rearrange the formula to calculate R: Rate = \(\frac{Simple Interest \times 100}{Principal \times Time}\) Substitute the values in the formula: Rate = \(\frac{60 \times 100}{300 \times \frac{1}{6}}\) Rate = \(\frac{6000}{50}\) = 120%

Compare the calculated rate with the given options

Our calculated rate of interest is 120%, which matches the option (c). Therefore, the correct answer is (c) 120%.

Key concepts

Interest Rate Calculation

Interest rate calculation is a critical part of financial transactions, particularly when assessing payment schemes like the one in the cellphone example. The interest rate essentially tells you how much extra money you will have to pay, as a percentage of the principal amount, for borrowing money over a specific period.
To calculate the interest rate, we use the formula for simple interest:

• Simple Interest (SI) = \(\frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\)

In our cellphone exercise, we first calculated the interest amount by taking the difference between the total cost for payments over time and the outright purchase price. Here, it was Rs. 60.
We then rearranged the simple interest formula to solve for the rate:

• Rate (R) = \(\frac{\text{Interest} \times 100}{\text{Principal} \times \text{Time}}\)

Using this formula, we found that the rate of interest in the example was \(120\%\). This helps us understand the extra percentage cost of opting for the delayed payment scheme.

Principal Amount

The principal amount is the initial sum of money on which interest is calculated. It's crucial to correctly identify this amount in any financial calculation, as it directly affects the interest calculation. In our cellphone example, the principal amount was the initial down payment made, which was Rs. 300.
This means that the interest, which represents the cost of borrowing the required funds to complete the purchase, is calculated on the Rs. 300 that remains unpaid initially. Identifying the principal correctly ensures the interest is calculated on the correct amount. This is key in making sound financial decisions. Remember that the principal amount can differ based on the context and the structure of payments.

Time Period in Years

Understanding how to convert the time period into years is an essential aspect of calculating simple interest. Time often isn't given directly in years, and we need to convert it for the interest formula.
In this situation, the time given was 2 months, which was converted into years for the calculation. This conversion is achieved by dividing the number of months by 12 (since there are 12 months in a year):

• Time in years = \(\frac{\text{Time in months}}{12}\)

In our example, 2 months becomes \(\frac{1}{6}\) of a year. Accurately converting time periods is vital for interest calculations, as it affects the outcomes significantly. Always ensure your time period is in the correct unit to avoid errors in financial calculations.

Payment Scheme Analysis

Analyzing payment schemes is a valuable skill, helping to outline how much extra you may have to pay when deferring payments.
The exercise provided a scenario with two payment options: an outright purchase at Rs. 600 or a split payment option with a down payment and a deferred amount. The latter option involved Rs. 360 due in two months, making the total Rs. 660.

• The objective here is to determine the financial implication of choosing the split payment option over the outright purchase.
• To determine the best financial decision, you calculate the interest charged, which, in this scenario, was found to be \(120\%\).

Through this analysis, we can see that while splitting payments might seem manageable, it can lead to substantial additional costs. It is always advisable to perform such calculations before making payment decisions to understand the financial impact fully.