On 5000, the rate of interest for first year is 20% and second year is 10% and difference between SI and CI for 1.5 years?

Options

A. ₹60
B. ₹ 50
C. ₹ 55
D. ₹65

Answer

To solve the problem of finding the difference between Simple Interest (SI) and Compound Interest (CI) for 1.5 years on a principal amount of Rs. 5000 with varying interest rates, we can follow these steps:

### Step-by-Step Solution:

**Step 1: Calculate the Simple Interest for 1.5 years.**

- For the first year, the rate of interest is 20%.
- For the second year, the rate of interest is 10%. However, since we are only considering 0.5 years of the second year, we will use half of the second year's rate.

**Calculation:**
- SI for the first year = Principal × Rate × Time
\[ SI_1 = 5000 \times \frac{20}{100} \times 1 = 1000 \]

- SI for the second year (for 0.5 years) = Principal × Rate × Time
\[ SI_2 = 5000 \times \frac{10}{100} \times 0.5 = 250 \]

- Total SI for 1.5 years:
\[ SI_{total} = SI_1 + SI_2 = 1000 + 250 = 1250 \]

**Step 2: Calculate the Compound Interest for 1.5 years.**

- For the first year, the interest is calculated on the principal.
- For the second year, the interest is calculated on the total amount after the first year.

**Calculation:**
- CI for the first year = Principal × Rate
\[ CI_1 = 5000 \times \frac{20}{100} = 1000 \]

- Amount after first year:
\[ A_1 = Principal + CI_1 = 5000 + 1000 = 6000 \]

- CI for the second year (for 0.5 years):
\[ CI_2 = A_1 \times \frac{10}{100} \times 0.5 = 6000 \times \frac{10}{100} \times 0.5 = 300 \]

- Total CI for 1.5 years:
\[ CI_{total} = CI_1 + CI_2 = 1000 + 300 = 1300 \]

**Step 3: Find the difference between CI and SI.**

- Difference = CI - SI
\[ Difference = 1300 - 1250 = 50 \]

### Final Answer:
The difference between Simple Interest and Compound Interest for 1.5 years is **Rs. 50**.

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