Sapna borrowed a certain sum of money, from Kavita under the following repayment scheme based on simple interest. 8% p.a. for the initial 2 years, 9.5% p.a.for the next 4 years, 11%p.a. for the next 2 years, 12% p.a. after the first 8 years. Find the amount which a sum of Rs. 9000 taken for 12 years becomes at the end of 12 years.

Options

A. Rs. 20160
B. Rs. 22350
C. Rs. 23470
D. Rs. 24567

Answer

To find the total amount Sapna owes after borrowing Rs. 9000 for 12 years under a simple interest scheme with varying interest rates, we can break down the calculation into steps based on the different interest rates for different time periods.

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
- The principal amount borrowed by Sapna is Rs. 9000.

2. **Breakdown the Time Period**:
- The total time period is 12 years, which can be divided as follows:
- First 2 years: 8% per annum
- Next 4 years: 9.5% per annum
- Next 2 years: 11% per annum
- Last 4 years: 12% per annum

3. **Calculate Simple Interest for Each Period**:
- **For the first 2 years at 8%**:
\[ \text{SI}_1 = P \times \frac{R_1}{100} \times T_1 = 9000 \times \frac{8}{100} \times 2 = 9000 \times 0.08 \times 2 = 1440 \]

- **For the next 4 years at 9.5%**:
\[ \text{SI}_2 = P \times \frac{R_2}{100} \times T_2 = 9000 \times \frac{9.5}{100} \times 4 = 9000 \times 0.095 \times 4 = 3420 \]

- **For the next 2 years at 11%**:
\[ \text{SI}_3 = P \times \frac{R_3}{100} \times T_3 = 9000 \times \frac{11}{100} \times 2 = 9000 \times 0.11 \times 2 = 1980 \]

- **For the last 4 years at 12%**:
\[ \text{SI}_4 = P \times \frac{R_4}{100} \times T_4 = 9000 \times \frac{12}{100} \times 4 = 9000 \times 0.12 \times 4 = 4320 \]

4. **Total Simple Interest (SI)**:
- Now, add all the simple interest amounts calculated:
\[ \text{Total SI} = \text{SI}_1 + \text{SI}_2 + \text{SI}_3 + \text{SI}_4 = 1440 + 3420 + 1980 + 4320 = 11160 \]

5. **Calculate the Total Amount (A)**:
- The total amount to be repaid after 12 years is given by:
\[ A = P + \text{Total SI} = 9000 + 11160 = 20160 \]

### Final Answer:
The amount which Rs. 9000 becomes at the end of 12 years is **Rs. 20,160**.

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