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The problem in the image is in Bengali and translates roughly to:

**Problem 34**: If 620,000 Taka is deposited in a bank at an annual interest rate of 5% with compound interest, find the amount in the bank at the end of 2 years and 6 months. Calculate the total interest earned by the bank.

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To solve this, we’ll go through these steps:

1. **Convert the time period**: Since 2 years and 6 months is 2.5 years, we’ll use \( t = 2.5 \) years.
2. **Use the compound interest formula**: 

   \[
   A = P \left(1 + \frac{r}{100}\right)^t
   \]
   
   where:
   - \( P = 620,000 \) Taka (the principal),
   - \( r = 5\% \) (the annual interest rate),
   - \( t = 2.5 \) years.

3. **Calculate the interest**: 

   Once we have the total amount \( A \), the interest earned \( I \) is:
   
   \[
   I = A - P
   \]

Let’s proceed with these calculations:

1. Plugging in the values:
   
   \[
   A = 620000 \times \left(1 + \frac{5}{100}\right)^{2.5}
   \]

2. Calculating \( A \) will give us the final amount, and then we subtract 620,000 to find the interest.

Would you like the exact calculations for each step, or do you have specific questions? 

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**Related Questions**:

1. What if the interest rate was different, say 7%?
2. How would the calculation change if the period were 3 years?
3. What would the total interest be if it was calculated using simple interest instead?
4. How would monthly compounding change the interest calculation?
5. How does compound interest differ fundamentally from simple interest?

**Tip**: Compound interest grows faster than simple interest because the interest is calculated on both the initial principal and the accumulated interest from previous periods.

A sum of 620,000 Taka is deposited in a bank at a 5% annual interest rate, compounded annually, for 2 years and 6 months. Find the total amount in the bank after this period and calculate the total interest earned.

Learn to calculate the compound interest for a principal of 620,000 Taka at a 5% annual rate over a period of 2 years and 6 months. This problem covers key financial math concepts, including exponential growth and interest calculations. Suitable for Grade 10 students.

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