Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to discharge her debt?

Answer

To find out how much Ratna will have to pay to the bank after 2 years to discharge her debt, we will calculate the compound interest on the loan amount. The formula for calculating the amount (A) after a certain time with compound interest is:

\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Where:
- \( A \) = Total amount after time \( t \)
- \( P \) = Principal amount (initial loan)
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

### Step 1: Identify the values
- Principal (P) = Rs 25000
- Rate of interest (r) = 8% per annum
- Time (t) = 2 years

### Step 2: Substitute the values into the formula
Now, we will substitute the identified values into the formula:

\[ A = 25000 \left(1 + \frac{8}{100}\right)^2 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \( \frac{8}{100} \):

\[ \frac{8}{100} = 0.08 \]

Now, substitute this back into the equation:

\[ A = 25000 \left(1 + 0.08\right)^2 \]

### Step 4: Calculate the value inside the parentheses
Now, calculate \( 1 + 0.08 \):

\[ 1 + 0.08 = 1.08 \]

### Step 5: Raise the result to the power of 2
Now, we will calculate \( (1.08)^2 \):

\[ (1.08)^2 = 1.1664 \]

### Step 6: Multiply by the principal amount
Now, we will multiply this result by the principal amount:

\[ A = 25000 \times 1.1664 \]

### Step 7: Calculate the final amount
Now, calculate the final amount:

\[ A = 25000 \times 1.1664 = 29160 \]

So, the total amount Ratna will have to pay to the bank after 2 years is Rs 29160.

### Final Answer:
**Ratna will have to pay Rs 29160 to the bank after 2 years.**

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