compound interest on a certain sum of money invested for 1.5 years at the rate of 10 percent per annum compounded half yearly is 5044

To find the principal sum of money invested, we can use the formula for compound interest:

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

Where:
- \( A \) is the amount of money accumulated after \( n \) periods, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual nominal interest rate (as a decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for, in years.

Given:
- The total amount \( A = P + \text{Interest} = P + 5044 \).
- The interest rate \( r = 10\% = 0.10 \).
- The interest is compounded half-yearly, so \( n = 2 \).
- The time period \( t = 1.5 \) years.

We need to find \( P \).

### Step 1: Calculate the amount after 1.5 years

Using the compound interest formula:

\[
A = P \left(1 + \frac{0.10}{2}\right)^{2 \times 1.5}
\]

Simplify:

\[
A = P \left(1 + 0.05\right)^{3} = P \times 1.157625
\]

### Step 2: Set up the equation with the known interest

The total interest earned is given as 5044, so:

\[
P \times 1.157625 = P + 5044
\]

### Step 3: Solve for \( P \)

Subtract \( P \) from both sides:

\[
P \times 0.157625 = 5044
\]

\[
P = \frac{5044}{0.157625} \approx 32000
\]

Thus, the principal sum of money invested is approximately **₹32,000**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does changing the compounding frequency affect the total interest earned?
2. What would the interest be if the rate was compounded quarterly?
3. How much would the total amount be after 2 years instead of 1.5 years?
4. How does simple interest compare with compound interest for the same rate and time period?
5. What happens if the interest rate increases to 12% per annum?

**Tip:** When dealing with compound interest, remember that increasing the frequency of compounding results in more interest earned over the same period.

Learn how to calculate compound interest on a principal sum of money invested for 1.5 years at a 10% annual rate compounded half yearly. Detailed step-by-step solution included. Suitable for advanced high school students and anyone interested in financial mathematics.

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