According to a new plan rolled out by HISP Bank , the rate of simple interest on the sum of money is `8%` pa for the first two years, `10%` pa for the next three years and `6%` pa for the period beyond the first five years. The simple interest accrued on a sum for a period of eight years is ₹12,800. Find the sum.

Options

A. 24000
B. 16000
C. 15000
D. 20000

Answer

To find the sum of money based on the given interest rates and the total interest accrued over eight years, we can break down the calculation into parts based on the different interest rates applicable for different time periods.

### Step-by-Step Solution:

1. **Identify the time periods and interest rates:**
- For the first 2 years, the interest rate is 8% per annum.
- For the next 3 years (years 3 to 5), the interest rate is 10% per annum.
- For the last 3 years (years 6 to 8), the interest rate is 6% per annum.

2. **Calculate the interest for each period:**
- Let the principal amount (sum) be denoted as \( P \).

- **Interest for the first 2 years:**
\[ \text{Interest}_1 = P \times \frac{8}{100} \times 2 = 0.16P \]

- **Interest for the next 3 years:**
\[ \text{Interest}_2 = P \times \frac{10}{100} \times 3 = 0.30P \]

- **Interest for the last 3 years:**
\[ \text{Interest}_3 = P \times \frac{6}{100} \times 3 = 0.18P \]

3. **Sum up the total interest accrued over the 8 years:**
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.16P + 0.30P + 0.18P = 0.64P \]

4. **Set the total interest equal to the given interest:**
According to the problem, the total interest accrued over 8 years is ₹12,800.
\[ 0.64P = 12800 \]

5. **Solve for \( P \):**
\[ P = \frac{12800}{0.64} = 20000 \]

### Final Answer:
The sum of money is ₹20,000.

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