Ram invested 50,000 rupees at 14% p.a. compounded half-yearly. What is the amount that Ram will get at the end of 9 months.

We are given:

- Principal (P) = ₹50,000
- Annual interest rate (R) = 14% p.a. (compounded half-yearly)
- Time (T) = 9 months
- Compound frequency: half-yearly

Since the interest is compounded half-yearly, we need to adjust the rate and time accordingly:

1. **Half-yearly rate of interest (R):**
   \[
   R = \frac{14}{2} = 7\% \text{ per half-year}
   \]

2. **Number of half-yearly periods (n):**
   \[
   n = \frac{9 \text{ months}}{6 \text{ months per half-year}} = 1.5 \text{ half-year periods}
   \]

Now, we can use the compound interest formula:

\[
A = P \left(1 + \frac{R}{100}\right)^n
\]

Where:
- \(A\) is the amount
- \(P\) is the principal
- \(R\) is the interest rate per period
- \(n\) is the number of periods

Substituting the values into the formula:

\[
A = 50,000 \left(1 + \frac{7}{100}\right)^{1.5}
\]

Let’s compute the final amount.The amount that Ram will receive at the end of 9 months, with interest compounded half-yearly, is approximately ₹55,340.83.

Would you like further details or clarifications?

Here are 5 related questions for practice:
1. How would the amount change if the interest rate was compounded quarterly instead?
2. What would be the amount if the time period was extended to 1 year?
3. How does compounding frequency affect the total amount received?
4. If the interest rate were 10% instead of 14%, what would be the new amount?
5. What is the difference between simple and compound interest over the same period?

**Tip:** The more frequent the compounding, the greater the total amount of interest earned!

Ram invested 50,000 rupees at 14% p.a. compounded half-yearly. What is the amount that Ram will get at the end of 9 months?

Discover how to calculate the compound interest on an investment of 50,000 rupees at 14% per annum, compounded half-yearly for 9 months. The solution includes the key formula, calculations, and related concepts, suitable for Grades 9-11 students.

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