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 determine the amount of money Mr. Perera should invest, we can use the **compound interest formula**:

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

Where:
- \(A\) is the final amount (Rs. 25,000),
- \(P\) is the initial investment (what we want to find),
- \(r\) 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 now until Kumara's 25th birthday, which is \(25 - 15 = 10\) years).

We need to solve for \(P\), the principal:

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

Substituting the values:

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

Let's calculate this.Mr. Perera should invest approximately **Rs. 11,409.67** today to provide Rs. 25,000 on Kumar's 25th birthday, assuming an interest rate of 8% compounded semi-annually.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How would the initial investment change if the interest rate were 6% instead of 8%?
2. What would be the final amount if Mr. Perera invests Rs. 15,000 instead of Rs. 11,409.67?
3. How much interest will Mr. Perera earn over the 10 years?
4. What if the interest is compounded quarterly instead of semi-annually? How would this affect the initial investment?
5. How does the time period of the investment affect the required principal?

**Tip:** The more frequently interest is compounded, the higher the final amount, due to the effect of compounding!

Mr. Perera's son Kumar has just completed 15 years of age. In order to provide a sum of Rs. 25,000 on Kumar'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.

Discover how to calculate the initial investment needed to provide Rs. 25,000 on Kumar's 25th birthday with an 8% interest rate compounded semi-annually. Learn key financial concepts like compound interest and exponential growth. Ideal for students in Grades 10-12.

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