Question

What is the sum of amount which gives Rs. 6300 as interest (@ \(7 \%\) per annum of simple interest in \(7 \frac{1}{2}\) years? (a) 36000 (b) 24000 (c) 63000 (d) 12000

Short answer

Answer: (d) 12000

Step-by-step solution

Write down the given information

We are given the following information: Simple Interest (SI) = Rs. 6300 Rate (R) = 7% per annum Time (T) = 7.5 years

Use the Simple Interest formula to solve for the principal amount (P)

We will be using the Simple Interest formula: Simple Interest (SI) = (Principal (P) * Rate (R) * Time (T)) / 100 Plugging in the given values: 6300 = (P * 7 * 7.5) / 100

Solve for P (Principal amount)

To find the principal amount P, we can rearrange the formula as follows: P = (6300 * 100) / (7 * 7.5) Now, calculate the value of P: P = (6300 * 100) / (7 * 7.5) = 12000 So, the principal amount (P) is Rs. 12000.

Choose the correct option

Now that we have found the principal amount to be Rs. 12000, we can choose the correct option among the given choices: (a) 36000 (b) 24000 (c) 63000 (d) 12000 The correct option is (d) 12000.

Key concepts

Simple Interest Formula

Understanding how to compute simple interest is crucial for managing personal finances and understanding basic financial instruments. The formula for calculating simple interest is remarkably straightforward and is given by:
\[\text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100}\]
In this formula,

• Principal (P) represents the initial amount of money either invested or loaned.
• Rate (R) is the interest rate per period, expressed as a percentage.
• Time (T) is the duration for which the money is invested or borrowed.

To find the interest earned or payable over a specific period, simply multiply the initial amount (P) by the interest rate (R) for the time duration (T), and then divide by 100 to account for the percentage. This formula is most commonly used for loans, savings, and investments that do not compound interest, making it a fundamental concept in finance.

Principal Amount

The term 'principal amount' refers to the initial sum of money that is invested, saved, or borrowed. It is the base upon which interest is calculated. If you deposit money into a savings account, take out a loan, or invest capital, this initial sum is what the bank, borrower, or financial entity uses to calculate the interest you will earn or owe.
For instance, if you deposit Rs. 5,000 in a savings account at an interest rate of 4% per annum, the Rs. 5,000 is your principal amount. When dealing with simple interest calculations, the principal remains constant over the entire period, unlike compound interest where the principal may vary as interest is added to the original sum.

Rate of Interest

The rate of interest is essentially the cost of borrowing money or the return one earns on an investment, typically presented as an annual percentage. This rate is a crucial component of most financial transactions involving credit or investments. A higher interest rate indicates a greater return on investment when you are the investor. Conversely, when you're borrowing, a higher rate means you will pay more over the life of the loan.
Returning to our earlier example, if the bank offers a 7% per annum interest rate on a savings account, then every year, you'll earn interest equal to 7% of your principal amount. When calculating simple interest, it is important to note that the rate does not compound, meaning it's applied to the original principal throughout the entire period.

Time Period in Interest Calculation

The time period in interest calculations is the duration over which the money is lent, invested, or borrowed. The duration will influence the amount of interest earned or paid. In the context of simple interest, time is typically measured in years, but it can be adjusted to months or days depending on the specifics of the financial product or agreement.
For simple interest calculations, it's common to see time designated in years because the rate of interest is usually annual. However, if the time period is not in whole years, it must be converted accordingly—7.5 years, which is also 7 years and 6 months, or 90 months, as an example. It's important to be accurate with the time period to ensure the interest calculation is correct.