The Initial Investment Scenario

Oct 13, 2025 by windailys.com 26 views

Introduction

In the world of finance, understanding interest rates and investment strategies is crucial for making informed decisions about where to invest your money. In this article, we will explore a scenario where Susan invested a certain amount of money in two schemes, A and B, which offer interest at the rates of 8% and 9% per annum, respectively. We will analyze how the interest rates affect the total annual interest she receives and discuss the implications of interchanging the amount of investments in the two schemes.

The Initial Investment Scenario

Let's assume that Susan invested a certain amount of money in scheme A, which offers an interest rate of 8% per annum, and scheme B, which offers an interest rate of 9% per annum. The total annual interest she received from both schemes is ₹ 1860.

Mathematical Representation

Let's denote the amount of money invested in scheme A as 'x' and the amount of money invested in scheme B as 'y'. The total annual interest received from both schemes can be represented as:

Interest from scheme A = 8% of x = 0.08x Interest from scheme B = 9% of y = 0.09y

The total annual interest received from both schemes is the sum of the interest from scheme A and scheme B:

Total annual interest = 0.08x + 0.09y = 1860

Solving the Equation

To find the values of x and y, we need to solve the equation:

0.08x + 0.09y = 1860

We can start by multiplying both sides of the equation by 100 to eliminate the decimals:

8x + 9y = 186000

Now, we can use the method of substitution or elimination to solve for x and y. Let's use the method of substitution.

Substitution Method

We can solve for x in terms of y by isolating x in the equation:

8x = 186000 - 9y x = (186000 - 9y) / 8

Now, substitute the expression for x into the original equation:

0.08((186000 - 9y) / 8) + 0.09y = 1860

Simplify the equation:

18600 - 0.72y + 0.09y = 1860

Combine like terms:

-0.63y = -16740

Divide both sides by -0.63:

y = 26620

Now that we have found the value of y, we can substitute it back into the expression for x:

x = (186000 - 9(26620)) / 8 x = (186000 - 239580) / 8 x = -53080 / 8 x = -6626

Interchanging the Amount of Investments

Now, let's assume that Susan interchanged the amount of investments in the two schemes. This means that she invested the amount of money that was originally invested in scheme A in scheme B, and vice versa.

New Investment Scenario

Let's denote the new amount of money invested in scheme A as 'x' and the new amount of money invested in scheme B as 'y'. The total annual interest received from both schemes is still ₹ 1860.

Mathematical Representation

The total annual interest received from both schemes can be represented as:

Interest from scheme A = 8% of x = 0.08x Interest from scheme B = 9% of y = 0.09y

The total annual interest received from both schemes is the sum of the interest from scheme A and scheme B:

Total annual interest = 0.08x + 0.09y = 1860

Solving the Equation

To find the values of x and y, we need to solve the equation:

0.08x + 0.09y = 1860

We can start by multiplying both sides of the equation by 100 to eliminate the decimals:

8x + 9y = 186000

Now, we can use the method of substitution or elimination to solve for x and y. Let's use the method of substitution.

Substitution Method

We can solve for x in terms of y by isolating x in the equation:

8x = 186000 - 9y x = (186000 - 9y) / 8

Now, substitute the expression for x into the original equation:

0.08((186000 - 9y) / 8) + 0.09y = 1860

Simplify the equation:

18600 - 0.72y + 0.09y = 1860

Combine like terms:

-0.63y = -16740

Divide both sides by -0.63:

y = 26620

Now that we have found the value of y, we can substitute it back into the expression for x:

x = (186000 - 9(26620)) / 8 x = (186000 - 239580) / 8 x = -53080 / 8 x = -6626

Comparison of the Two Scenarios

In the initial investment scenario, Susan invested a certain amount of money in scheme A and scheme B, which offer interest rates of 8% and 9% per annum, respectively. She received a total annual interest of ₹ 1860.

In the new investment scenario, Susan interchanged the amount of investments in the two schemes. She invested the amount of money that was originally invested in scheme A in scheme B, and vice versa. The total annual interest received from both schemes is still ₹ 1860.

Conclusion

In conclusion, the interest rates of the two schemes affect the total annual interest received by Susan. In the initial investment scenario, she received a total annual interest of ₹ 1860. In the new investment scenario, she interchanged the amount of investments in the two schemes, and the total annual interest received from both schemes is still ₹ 1860.

Key Takeaways

The interest rates of the two schemes affect the total annual interest received by Susan.
In the initial investment scenario, Susan received a total annual interest of ₹ 1860.
In the new investment scenario, Susan interchanged the amount of investments in the two schemes, and the total annual interest received from both schemes is still ₹ 1860.

Recommendations

Investors should consider the interest rates of different schemes before investing their money.
Interchanging the amount of investments in different schemes can affect the total annual interest received.
Investors should carefully evaluate the risks and benefits of different investment options before making a decision.

Final Thoughts

Introduction

In our previous article, we explored a scenario where Susan invested a certain amount of money in two schemes, A and B, which offer interest rates of 8% and 9% per annum, respectively. We analyzed how the interest rates affect the total annual interest she receives and discussed the implications of interchanging the amount of investments in the two schemes. In this article, we will answer some frequently asked questions related to Susan's investment scenario.

Q&A

Q: What is the total annual interest received by Susan in the initial investment scenario?

A: In the initial investment scenario, Susan received a total annual interest of ₹ 1860.

Q: How does the interest rate of scheme A affect the total annual interest received by Susan?

A: The interest rate of scheme A affects the total annual interest received by Susan. In the initial investment scenario, the interest rate of scheme A is 8%, which means that Susan receives 8% of the amount invested in scheme A as interest.

Q: What happens if Susan interchanges the amount of investments in the two schemes?

A: If Susan interchanges the amount of investments in the two schemes, the total annual interest received from both schemes remains the same, which is ₹ 1860.

Q: How does the interest rate of scheme B affect the total annual interest received by Susan?

A: The interest rate of scheme B affects the total annual interest received by Susan. In the initial investment scenario, the interest rate of scheme B is 9%, which means that Susan receives 9% of the amount invested in scheme B as interest.

Q: Can Susan receive a higher total annual interest by investing more money in scheme B?

A: Yes, Susan can receive a higher total annual interest by investing more money in scheme B. However, this would require her to invest a larger amount of money in scheme B, which may not be feasible for her.

Q: What is the relationship between the amount invested in scheme A and the amount invested in scheme B?

A: The amount invested in scheme A and the amount invested in scheme B are related through the total annual interest received from both schemes. In the initial investment scenario, the total annual interest received from both schemes is ₹ 1860, which is the sum of the interest from scheme A and scheme B.

Q: Can Susan receive a higher total annual interest by investing more money in scheme A?

A: Yes, Susan can receive a higher total annual interest by investing more money in scheme A. However, this would require her to invest a larger amount of money in scheme A, which may not be feasible for her.

Q: What are the implications of interchanging the amount of investments in the two schemes?

A: The implications of interchanging the amount of investments in the two schemes are that the total annual interest received from both schemes remains the same, which is ₹ 1860. However, the amount invested in scheme A and the amount invested in scheme B may change.

Q: Can Susan receive a higher total annual interest by investing in a different scheme?

A: Yes, Susan can receive a higher total annual interest by investing in a different scheme that offers a higher interest rate. However, this would require her to invest in a different scheme, which may not be feasible for her.

Conclusion

In conclusion, Susan's investment scenario is a complex one, and there are many factors that affect the total annual interest she receives. By understanding the interest rates of the two schemes and the implications of interchanging the amount of investments in the two schemes, investors can make informed decisions about where to invest their money.

Key Takeaways

The interest rates of the two schemes affect the total annual interest received by Susan.
Interchanging the amount of investments in the two schemes can affect the total annual interest received.
Investors should carefully evaluate the risks and benefits of different investment options before making a decision.

Recommendations

Investors should consider the interest rates of different schemes before investing their money.
Interchanging the amount of investments in different schemes can affect the total annual interest received.
Investors should carefully evaluate the risks and benefits of different investment options before making a decision.