Question

A man borrows Rs. 4000 and pays back after 5 years at \(15 \%\) simple interest. The amount paid by the man is : (a) Rs. 1800 (b) Rs. 4800 (c) Rs. 7500 (d) Rs. 7000

Short answer

a) Rs. 6000 b) Rs. 6500 c) Rs. 6750 d) Rs. 7000 Answer: d) Rs. 7000

Step-by-step solution

Convert the rate into decimal form

To convert the rate from percentage to decimal, divide the given rate by 100. Rate in decimal = \(\frac{15}{100}\) = 0.15

Calculate the simple interest

Now that we have the rate in decimal form, we can use the formula for simple interest: Simple Interest = Principal × Rate × Time Plugging in the values, we have: Simple Interest = 4000 × 0.15 × 5 Simple Interest = Rs. 3000

Find the total amount paid

To find the total amount paid by the man, add the simple interest to the principal amount: Total Amount = Principal + Simple Interest Total Amount = 4000 + 3000 Total Amount = Rs. 7000 The man paid Rs. 7000 in total, so the correct answer is option (d).

Key concepts

Simple Interest Formula

Understanding the simple interest formula is crucial for anyone dealing with loans, investments, or any financial scenarios where money is borrowed for a specific period. The formula is given by
\[ \text{Simple Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \]
This formula calculates the interest incurred over a certain period without compounding. Here, the Principal is the initial amount of money borrowed or invested, the Rate is the interest rate per period, and Time is the duration for which the money is borrowed or invested. To put it into practice, for example, if a man borrows Rs. 4000 at an annual interest rate of 15% for 5 years, the interest calculation would be Rs. 3000, considering no payments are made until the end of the 5-year period. Simple interest is straightforward because it does not account for the interest on the interest earned or paid, unlike compound interest.

Converting Percentages to Decimals

When working with interest rates in financial calculations, converting percentages to decimals is a fundamental skill. A percentage represents a number as a fraction of 100 and to convert it to a decimal, you simply divide by 100. For example,

Converting 15%

You would divide 15 by 100:\[ \frac{15}{100} = 0.15 \]
Thus, 15% is equivalent to 0.15 in decimal form. This is important in calculations for the simple interest formula, where the decimal rate is needed to determine the exact amount of interest accrued over time. Remembering this basic conversion is essential as it is routinely used in various mathematical and financial contexts.

Calculating Total Repayment

Calculating the total repayment on a loan or investment involves summing the principal amount with the accrued interest. Once you have figured out the simple interest using the appropriate formula, the next step is to add that interest to the original amount (principal) to obtain the total repayment amount. As seen in the textbook exercise,

Total Repayment Calculation

The simple interest accrued over 5 years on Rs. 4000 is Rs. 3000. To find the total repayment amount, you simply combine the original borrowed amount with the interest:\[ \text{Total Amount} = \text{Principal} + \text{Simple Interest} \]\[ \text{Total Amount} = Rs. 4000 + Rs. 3000 \]\[ \text{Total Amount} = Rs. 7000 \]
This total is what the borrower would pay back at the end of the loan term. In summary, the total repayment gives a complete picture of the financial commitment involved in a loan or investment and is vital for personal or business financial planning.