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 fixed sum Mr. Perera should invest, we can use the compound interest formula:

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

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

Now, rearrange the formula to solve for \(P\):

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

Substituting the values:

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

Let's compute this.The amount Mr. Perera should invest is approximately Rs. 11,409.67 to provide Rs. 25,000 on Kumar's 25th birthday, assuming the account earns 8% interest compounded semi-annually.

Would you like more details or have any questions about this?

Here are 5 related questions for deeper understanding:
1. How would the required investment change if the interest rate was compounded quarterly?
2. What would be the total interest earned on the investment over the 10-year period?
3. How does semi-annual compounding compare to annual compounding for this scenario?
4. What would the investment be if Mr. Perera wanted Rs. 50,000 instead of Rs. 25,000?
5. How would the calculation differ if the interest rate were variable instead of fixed?

**Tip:** The more frequently interest is compounded, the higher the amount grows due to the effect of compounding interest on accumulated interest.

Learn how to calculate the initial investment needed to grow Rs. 25,000 over 10 years with 8% interest compounded semi-annually. This problem explains key concepts of compound interest and exponential growth, suitable for Grades 10-12 students.

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