Mr. Perera's son Kumar has just completed 15 years of age. In order to provide a sum of Rs. 25,000 on Kumara's 25th Birthday, Mr. Perera has decided to invest a fixed sum of money. Calculate the amount of money that should be invested assuming the account earns interest at a rate of 8% compounded semi-annually.

To solve this problem, we need to calculate the present value of an investment that will grow to Rs. 25,000 in 10 years at an interest rate of 8% compounded semi-annually. 

### Step-by-Step Solution

1. **Identify the known values:**
   - Future Value (\(FV\)) = Rs. 25,000
   - Interest rate per annum (\(r\)) = 8% compounded semi-annually
   - Number of compounding periods per year = 2
   - Time period (\(t\)) = 10 years (from Kumar's current age of 15 to 25)
   
2. **Convert the annual interest rate to the semi-annual rate:**
   \[
   \text{Semi-annual interest rate} = \frac{8\%}{2} = 4\% = 0.04
   \]

3. **Calculate the total number of compounding periods:**
   \[
   n = t \times \text{Number of compounding periods per year} = 10 \times 2 = 20
   \]

4. **Use the formula for the Present Value (PV) of an investment:**

\[
PV = \frac{FV}{(1 + r/n)^{nt}}
\]

Plug in the values:

\[
PV = \frac{25000}{(1 + 0.04)^20}
\]

Let's calculate this amount.The amount of money Mr. Perera should invest is approximately **Rs. 11,409.67** to ensure that it grows to Rs. 25,000 by Kumar's 25th birthday, assuming an 8% interest rate compounded semi-annually.

### Would you like more details or have any questions?

### Related Questions:
1. How would the amount change if the interest were compounded quarterly instead?
2. What if Mr. Perera wants the money to grow to Rs. 30,000 instead of Rs. 25,000?
3. How much would the investment be worth in 15 years at the same interest rate?
4. What is the difference between compound interest and simple interest for this investment?
5. How does changing the compounding frequency affect the final amount?

**Tip:** When dealing with compound interest, the more frequently interest is compounded, the greater the final amount will be due to the effect of compounding.

Learn how to calculate the present value of an investment to grow to Rs. 25,000 in 10 years at an interest rate of 8% compounded semi-annually. This detailed guide includes key financial mathematics concepts, formulas, and step-by-step instructions. Suitable for students in Grades 10-12.

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