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 find the principal amount that will amount to Rs 9,856 in two years with different rates of interest for each year, we can use the compound interest formula. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We need to find the principal (P) that will amount to Rs 9,856 after 2 years with interest rates of 10% for the first year and 12% for the second year.

### Step 2: Write Down the Formula
The formula for compound interest when different rates are applied for successive years is:

\[ A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \]

Where:
- \( A \) is the amount after the time period (Rs 9,856)
- \( P \) is the principal amount (which we need to find)
- \( r_1 \) is the interest rate for the first year (10%)
- \( r_2 \) is the interest rate for the second year (12%)

### Step 3: Substitute the Values
Substituting the known values into the formula, we have:

\[ 9856 = P \left(1 + \frac{10}{100}\right) \left(1 + \frac{12}{100}\right) \]

This simplifies to:

\[ 9856 = P \left(1 + 0.10\right) \left(1 + 0.12\right) \]

\[ 9856 = P \left(1.10\right) \left(1.12\right) \]

### Step 4: Calculate the Multiplication
Now, calculate \( 1.10 \times 1.12 \):

\[ 1.10 \times 1.12 = 1.232 \]

### Step 5: Substitute Back into the Equation
Now, substitute back into the equation:

\[ 9856 = P \times 1.232 \]

### Step 6: Solve for Principal (P)
To find \( P \), rearrange the equation:

\[ P = \frac{9856}{1.232} \]

Now, perform the division:

\[ P = 8000 \]

### Final Answer
The principal amount is Rs 8,000.

---