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 calculate the amount of money that Mr. Perera should invest now to have Rs. 25,000 on Kumar's 25th birthday, we can use the formula for compound interest. The formula is:

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

Where:
- \( A \) is the future value of the investment (Rs. 25,000),
- \( P \) is the present value or the amount to be invested,
- \( r \) is the annual interest rate (8% or 0.08),
- \( n \) is the number of times the interest is compounded per year (semi-annually, so \( n = 2 \)),
- \( t \) is the time in years (from Kumar's current age of 15 to 25, so \( t = 10 \)).

We need to solve for \( P \).

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

Now, plug in the values:

\[
P = \frac{25000}{\left(1 + \frac{0.08}{2}\right)^{2 \times 10}}
\]

\[
P = \frac{25000}{\left(1 + 0.04\right)^{20}}
\]

\[
P = \frac{25000}{\left(1.04\right)^{20}}
\]

Let's calculate the value of \( P \).The amount of money that Mr. Perera should invest now to have Rs. 25,000 on Kumar's 25th birthday, assuming an interest rate of 8% compounded semi-annually, is approximately **Rs. 11,409.67**.

Would you like further details or have any questions? 

Here are five related questions you might find interesting:
1. How would the investment amount change if the interest rate were 10% instead of 8%?
2. What if the interest was compounded quarterly instead of semi-annually?
3. How much interest will the investment earn over the 10-year period?
4. What if Mr. Perera wanted to save Rs. 50,000 instead of Rs. 25,000?
5. How does the compounding frequency affect the final amount?

**Tip:** The more frequently the interest is compounded, the higher the final amount will be, due to the effects of compounding interest on previous interest amounts.

Learn how to calculate the amount of money Mr. Perera should invest now to have Rs. 25,000 on Kumar's 25th birthday, assuming an interest rate of 8% compounded semi-annually. Detailed step-by-step solution provided.

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