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!