A young man started deposit in his savings account on his 16th birthday by depositing 30 rupees. If he deposit 30 rupees every 6 months there after he at 25 Yr age. What amount he has to be credit, if the bank pay 4%interest  compounded semiannually 

The problem involves calculating the future value of a series of deposits with compound interest. The deposits are made semiannually (every 6 months), and interest is compounded semiannually as well. Here's how to solve the problem step by step.

### 1. Key information:
- Initial age: 16 years
- Final age: 25 years
- Total number of years: \(25 - 16 = 9\) years
- Number of deposits per year: 2 (since deposits are made every 6 months)
- Number of deposit periods (semiannually): \(9 \times 2 = 18\)
- Deposit amount: ₹30
- Interest rate: 4% annually compounded semiannually (2% per 6 months, as \( \frac{4\%}{2} = 2\%\))

### 2. Formula:
We use the future value of a series formula for compound interest, which is:

\[
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \times (1 + r)
\]

Where:
- \(FV\) = future value (what we need to find),
- \(P\) = deposit amount (₹30),
- \(r\) = semiannual interest rate (2% or 0.02),
- \(n\) = number of periods (18 semiannual periods).

### 3. Plugging in the values:
\[
FV = 30 \times \left(\frac{(1 + 0.02)^{18} - 1}{0.02}\right) \times (1 + 0.02)
\]

Let's calculate this step-by-step.The total amount in the savings account when the man turns 25 will be approximately ₹655.22.

Would you like a detailed breakdown of the steps, or do you have any further questions?

Here are 5 related questions you might find helpful:
1. How would the total amount change if the interest rate were 5%?
2. What happens if the deposits were made annually instead of semiannually?
3. How would the total amount change if the deposits were ₹50 every 6 months instead of ₹30?
4. How does increasing the deposit frequency (e.g., monthly deposits) affect the final amount?
5. What would happen if no interest was paid by the bank?

**Tip:** The longer the period of compounding, the greater the effect of interest on the final amount, thanks to compound interest.

A young man started deposit in his savings account on his 16th birthday by depositing 30 rupees. If he deposit 30 rupees every 6 months thereafter, what amount will he have at 25 years of age, if the bank pays 4% interest compounded semiannually?

Learn how to calculate the future value of a savings account with semiannual deposits and compound interest. This problem covers key concepts like compound interest, future value of annuities, and series calculations. Suitable for high school students (Grades 10-12).

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