Find the amount of 12000 after 2 years, compounded annually the rate of interset being 5% P.a. during the first year and 6% p.a during the second year. Also, find the compound interset.

Answer

To solve the problem of finding the amount of ₹12,000 after 2 years compounded annually at different rates of interest, we will follow these steps:

### Step 1: Calculate the Amount after the First Year
- **Principal (P)** = ₹12,000
- **Rate of Interest for the First Year (R1)** = 5% per annum
- **Time (T1)** = 1 year

Using the formula for compound interest:
\[ A_1 = P \times \left(1 + \frac{R1}{100}\right)^{T1} \]
Substituting the values:
\[ A_1 = 12000 \times \left(1 + \frac{5}{100}\right)^{1} \]
\[ A_1 = 12000 \times \left(1 + 0.05\right) = 12000 \times 1.05 = 12600 \]

### Step 2: Calculate the Amount after the Second Year
Now, the amount after the first year becomes the principal for the second year.
- **New Principal (P)** = ₹12,600 (amount from the first year)
- **Rate of Interest for the Second Year (R2)** = 6% per annum
- **Time (T2)** = 1 year

Using the same formula for compound interest:
\[ A_2 = P \times \left(1 + \frac{R2}{100}\right)^{T2} \]
Substituting the values:
\[ A_2 = 12600 \times \left(1 + \frac{6}{100}\right)^{1} \]
\[ A_2 = 12600 \times \left(1 + 0.06\right) = 12600 \times 1.06 = 13356 \]

### Step 3: Calculate the Compound Interest
Now, we find the compound interest by subtracting the original principal from the final amount:
\[ \text{Compound Interest} = A_2 - \text{Principal} \]
Substituting the values:
\[ \text{Compound Interest} = 13356 - 12000 = 1356 \]

### Final Results
- **Amount after 2 years**: ₹13,356
- **Compound Interest**: ₹1,356

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