What principal will amount to Rs 9,856 in two years, if the rates of interest for successive years are 10% and 12% respectively ?

Answer

To solve the problem of finding the principal amount that will amount to Rs 9,856 in two years with successive interest rates of 10% and 12%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Amount (A) = Rs 9,856
- Time (t) = 2 years
- Rate of interest for the first year (R1) = 10%
- Rate of interest for the second year (R2) = 12%

2. **Use the Compound Interest Formula:**
The formula for compound interest when the rates are different for successive years is:
\[ A = P \times \left(1 + \frac{R1}{100}\right) \times \left(1 + \frac{R2}{100}\right) \]
Here, we need to rearrange it to find the principal (P):
\[ P = \frac{A}{\left(1 + \frac{R1}{100}\right) \times \left(1 + \frac{R2}{100}\right)} \]

3. **Substitute the Values into the Formula:**
Substitute A, R1, and R2 into the formula:
\[ P = \frac{9856}{\left(1 + \frac{10}{100}\right) \times \left(1 + \frac{12}{100}\right)} \]
Simplifying the rates:
\[ P = \frac{9856}{\left(1 + 0.10\right) \times \left(1 + 0.12\right)} = \frac{9856}{1.10 \times 1.12} \]

4. **Calculate the Denominator:**
Calculate \(1.10 \times 1.12\):
\[ 1.10 \times 1.12 = 1.232 \]

5. **Calculate the Principal (P):**
Now substitute back into the equation:
\[ P = \frac{9856}{1.232} \]
Performing the division:
\[ P \approx 8000 \]

6. **Final Answer:**
Therefore, the principal amount is Rs 8000.