Veer inyested Rs. 21000 in a scheme on compound interest, which offered interest at the rate `14(2)/(7)%` for first year, `12(1)/(2)%` of second year and `11(1)/(9)`% for third a year. Then find how much interest will Veer get after three year on his principle?

Options

A. 7500 Rs.
B. 9000 Rs.
C. 8000 Rs.
D. 8500 Rs.

Answer

To solve the problem step by step, we will calculate the compound interest for each year based on the given interest rates.

### Step 1: Convert the mixed fractions to improper fractions
- For the first year, the interest rate is \(14 \frac{2}{7}\%\).
- Convert to improper fraction: \(14 \frac{2}{7} = \frac{14 \times 7 + 2}{7} = \frac{98 + 2}{7} = \frac{100}{7}\%\).

- For the second year, the interest rate is \(12 \frac{1}{2}\%\).
- Convert to improper fraction: \(12 \frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{24 + 1}{2} = \frac{25}{2}\%\).

- For the third year, the interest rate is \(11 \frac{1}{9}\%\).
- Convert to improper fraction: \(11 \frac{1}{9} = \frac{11 \times 9 + 1}{9} = \frac{99 + 1}{9} = \frac{100}{9}\%\).

### Step 2: Calculate the amount after each year
1. **First Year:**
- Principal = Rs. 21,000
- Interest for the first year = \( \frac{100}{7}\% \) of 21,000
- Amount after first year = \( 21,000 \times \left(1 + \frac{100}{700}\right) = 21,000 \times \frac{8}{7} = 24,000 \)

2. **Second Year:**
- New Principal = Rs. 24,000
- Interest for the second year = \( \frac{25}{2}\% \) of 24,000
- Amount after second year = \( 24,000 \times \left(1 + \frac{25}{200}\right) = 24,000 \times \frac{9}{8} = 27,000 \)

3. **Third Year:**
- New Principal = Rs. 27,000
- Interest for the third year = \( \frac{100}{9}\% \) of 27,000
- Amount after third year = \( 27,000 \times \left(1 + \frac{100}{900}\right) = 27,000 \times \frac{10}{9} = 30,000 \)

### Step 3: Calculate the total interest earned
- Total amount after three years = Rs. 30,000
- Principal amount = Rs. 21,000
- Total interest earned = Total amount - Principal = \( 30,000 - 21,000 = 9,000 \)

### Final Answer:
Veer will get Rs. 9,000 as interest after three years.

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