Understanding Simple Interest in Real-Life Applications: A Case Study on Raj’s Borrowing

Simple interest is a fundamental concept in the field of finance and is commonly applied in various real-life scenarios. Let's delve into a case study involving Raj, who borrowed a total of Rs. 3500 from two different money lenders at varying interest rates. By understanding the principles of simple interest, we can solve for the specific amount Raj borrowed from each lender.

Problem Statement

Raj borrowed a total of Rs. 3500 from two money lenders at simple interest rates. He paid 5% per annum (p.a.) for one loan and 10% p.a. for the other. The total interest paid for two years was Rs. 500. The question is, how much did he borrow at the 10% rate?

Solving the Problem

To find the amount borrowed at 10%, we can set up and solve a system of equations. Let:

x the amount borrowed at 5 p.a. y the amount borrowed at 10 p.a.

Step 1: Set Up Equations

We know two key pieces of information from the problem:

The total amount borrowed is x y 3500 The total interest paid for two years is 0.05x(2) 0.10y(2) 500

Simplifying the second equation:

0.1 0.20y 500

Step 2: Solve for One Variable

First, solve Equation 1 for y:

y 3500 - x

Step 3: Substitute into the Second Equation

Substitute y into the simplified interest equation:

0.1x 0.2(3500 - x) 500

Distribute and simplify:

0.1x 700 - 0.2x 500

-0.1x 700 500

Step 4: Solve for x

-0.1x 500 - 700

-0.1x -200

x frac{-200}{-0.1} 2000

Step 5: Find y

Substitute x back into the equation for y:

y 3500 - 2000 1500

Conclusion

Raj borrowed Rs. 1500 at the 10% interest rate.

Additional Case Study

Another Similar Problem

Suppose Raj decided that instead of borrowing at 5% or 10%, he borrowed Rs. 10 from one lender at 7%. We need to figure out the second amount borrowed and the interest rates involved.

Scenario

Let the amount borrowed from the lender at 7% be X.

Step 1: Calculate Interest for Each Loan

For the loan at 7%:

Simple Interest frac{PNR}{100} frac{X cdot 7 cdot 2}{100} 0.14X

For the loan at 5%:

Simple Interest frac{PNR}{100} frac{(2500 - X) cdot 5 cdot 2}{100} 250 - 0.1X

Total interest paid:

0.14X 250 - 0.1X 275

Step 2: Solve for X

0.04X 250 275

0.04X 275 - 250

0.04X 25

X frac{25}{0.04} 625

Conclusion

Raj borrowed Rs. 1875 at 7% from the lender and Rs. 625 at 5% from the other lender.

Understanding these scenarios helps in applying and solving practical problems involving simple interest, which is crucial in financial planning and decision-making.