Amazonia, an online shopping portal, introduces two schemes for their customers, during a sale, on a LED TV whose price is Rs. 60,000. In scheme 1 they sell the TV at 25% discount and in scheme 2 they sell it at a down payment of Rs. 20,000 and four installments of Rs. 10,000 payable at intervals of a year. Assuming that Amazonia invests its money at a compound interest of 20% compounded annually, which offer is more profitable for them and by how much, at the end of four

To determine which scheme is more profitable for Amazonia, we need to analyze the revenue generated from both schemes and compare them, factoring in the time value of money using the compound interest rate provided.

### **Scheme 1: 25% Discount**

- **Original price of TV** = Rs. 60,000
- **Discount** = 25% of 60,000 = 0.25 × 60,000 = Rs. 15,000
- **Selling price under Scheme 1** = 60,000 - 15,000 = Rs. 45,000

Amazonia receives Rs. 45,000 upfront. To determine its future value after 4 years with 20% annual compound interest:

\[
\text{Future Value} = \text{Present Value} \times (1 + \text{interest rate})^n
\]

\[
\text{Future Value} = 45,000 \times (1 + 0.20)^4
\]

\[
\text{Future Value} = 45,000 \times 1.20^4
\]

\[
\text{Future Value} = 45,000 \times 2.0736 = Rs. 93,312
\]

### **Scheme 2: Down Payment and Installments**

- **Down payment** = Rs. 20,000
- **Installments**: Rs. 10,000 per year for 4 years

1. **Down Payment (Rs. 20,000) Future Value** (after 4 years):
   \[
   \text{Future Value} = 20,000 \times (1 + 0.20)^4 = 20,000 \times 2.0736 = Rs. 41,472
   \]

2. **First Installment (Rs. 10,000) Future Value** (after 3 years):
   \[
   \text{Future Value} = 10,000 \times (1 + 0.20)^3 = 10,000 \times 1.728 = Rs. 17,280
   \]

3. **Second Installment (Rs. 10,000) Future Value** (after 2 years):
   \[
   \text{Future Value} = 10,000 \times (1 + 0.20)^2 = 10,000 \times 1.44 = Rs. 14,400
   \]

4. **Third Installment (Rs. 10,000) Future Value** (after 1 year):
   \[
   \text{Future Value} = 10,000 \times (1 + 0.20)^1 = 10,000 \times 1.20 = Rs. 12,000
   \]

5. **Fourth Installment (Rs. 10,000) Future Value** (immediately at the end of the fourth year):
   \[
   \text{Future Value} = 10,000 \times (1 + 0.20)^0 = 10,000 \times 1 = Rs. 10,000
   \]

**Total Future Value in Scheme 2**:

\[
\text{Total Future Value} = 41,472 + 17,280 + 14,400 + 12,000 + 10,000 = Rs. 95,152
\]

### **Comparison of Profitability**

- **Scheme 1 Future Value**: Rs. 93,312
- **Scheme 2 Future Value**: Rs. 95,152

**Difference** = 95,152 - 93,312 = Rs. 1,840

### **Conclusion**
Scheme 2 is more profitable for Amazonia by Rs. 1,840 at the end of four years.

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How would the profitability change if the compound interest rate was different?
2. What if the installment payment intervals were reduced to half-yearly? How would this affect the future value?
3. How does the profitability change if the discount in Scheme 1 is increased to 30%?
4. What would be the outcome if the number of installments in Scheme 2 was increased to 5?
5. How would inflation impact the profitability analysis between these two schemes?

**Tip:** Always consider the time value of money when evaluating different payment options, especially for long-term investments.

Explore the profitability comparison of two sale schemes for an LED TV on Amazonia. Scheme 1 offers a 25% discount, while Scheme 2 involves a down payment and installments with compound interest at 20% annually. Analyze which scheme yields higher profitability after four years.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation