Question 5.

Total Marks: 20

Read the following sentences and answer the question that follows based on all or few of these statements. Note that all statements are true but may in may not be useful to reach the desired answer

1. Four years ago, Sahil invested 35,000 INR in an investment firm 2. Sahil's investment in the firm provided him with a 10% annual Interest on his

investments. 3. Over the years, Sahil reinvested the interest gain to maximise his returns

4. Tanya, Sahil's sister, made her investment 3 years ago. 5. Tanya Invested 20,000 INR in her chosen investment opportunity.

6. The investment offered to Tanya was subject to an annual compound interest of 20%.

7. Both Sahil and Tanya aimed to grow their initial investmerits through different interest structures.

8. Sahil's investment used a simple interest model, while Tanya's investment used a compound interest model.

9. Sahil's investment firm calculated interest annually based on the initial

investment amount. 10. In contrast, Tanya's compound interest was calculated annually, including the

interest on interest from previous years. 11. Sahil and Tanya monitored the growth of their investments over the years.

12. Comparing the performance of their investments allowed Sahil and Tanya to gain insights into the impact of different interest structures on their returns

Find the total interest earned by the pair.

To find the total interest earned by Sahil and Tanya, we'll need to calculate the interest earned by each based on the information provided.

### Sahil's Investment

**Details:**
- Initial Investment: INR 35,000
- Interest Rate: 10% per annum
- Duration: 4 years
- Interest Model: Simple Interest

**Simple Interest Calculation:**

\[ \text{Simple Interest (SI)} = P \times R \times T \]

Where:
- \( P \) is the principal amount (INR 35,000)
- \( R \) is the annual interest rate (10% or 0.10)
- \( T \) is the time period (4 years)

\[ \text{SI} = 35,000 \times 0.10 \times 4 \]
\[ \text{SI} = 35,000 \times 0.40 \]
\[ \text{SI} = 14,000 \]

So, Sahil earned a total interest of INR 14,000 over 4 years.

### Tanya's Investment

**Details:**
- Initial Investment: INR 20,000
- Interest Rate: 20% per annum
- Duration: 3 years
- Interest Model: Compound Interest

**Compound Interest Calculation:**

\[ A = P \left(1 + \frac{R}{n}\right)^{nT} \]

Where:
- \( P \) is the principal amount (INR 20,000)
- \( R \) is the annual interest rate (20% or 0.20)
- \( n \) is the number of times interest is compounded per year (since it's annually, \( n = 1 \))
- \( T \) is the time period (3 years)

\[ A = 20,000 \left(1 + \frac{0.20}{1}\right)^{1 \times 3} \]
\[ A = 20,000 \left(1 + 0.20\right)^3 \]
\[ A = 20,000 \left(1.20\right)^3 \]
\[ A = 20,000 \times 1.728 \]
\[ A = 34,560 \]

The total amount after 3 years is INR 34,560.

**Total Interest Earned:**

\[ \text{Total Interest} = A - P \]
\[ \text{Total Interest} = 34,560 - 20,000 \]
\[ \text{Total Interest} = 14,560 \]

So, Tanya earned a total interest of INR 14,560 over 3 years.

### Total Interest Earned by Sahil and Tanya Combined

\[ \text{Total Interest Earned} = \text{Interest Earned by Sahil} + \text{Interest Earned by Tanya} \]
\[ \text{Total Interest Earned} = 14,000 + 14,560 \]
\[ \text{Total Interest Earned} = 28,560 \]

Therefore, the total interest earned by Sahil and Tanya combined is INR 28,560.

Would you like further details or have any questions? Here are some related questions to expand on this information:

1. What would be the total interest if Sahil's interest was compounded annually?
2. How much more interest would Tanya earn if her investment period was extended to 5 years?
3. What if Tanya's investment rate was reduced to 15%? How would that affect her total interest?
4. How would Sahil's total interest change if he reinvested his interest annually like Tanya?
5. How does the difference in interest models affect the overall returns for Sahil and Tanya?
6. What is the effective annual rate of Tanya's investment?
7. How would the interest earned by Tanya change if she invested INR 25,000 instead of INR 20,000?
8. What impact does the initial investment amount have on the total interest earned over time?

**Tip:** Understanding the difference between simple and compound interest is crucial in making informed investment decisions, as compound interest typically yields higher returns over time due to interest on interest.

Discover how Sahil and Tanya earned interest on their investments using simple and compound interest calculations. Sahil invested INR 35,000 with 10% annual interest, while Tanya invested INR 20,000 with 20% compound interest annually. Learn how to compute their total interest earnings over their investment periods.

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