The problem is asking to calculate the future value of a sum of ₹5,000 invested for two years with interest compounding semi-annually and quarterly at an annual interest rate of 12%.

Future Value Formula for Compound Interest:

The formula for compound interest is:

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

Where:

• $A$ = Future value
• $P$ = Principal amount (₹5,000)
• $r$ = Annual interest rate (12% or 0.12)
• $n$ = Number of times the interest is compounded per year
• $t$ = Time the money is invested for (2 years)

Case 1: Semi-Annual Compounding

For semi-annual compounding, the interest is compounded twice a year, so:

• $n = 2$
• $t = 2$ years

Substitute these values into the formula:

$A_{\text{semi-annual}} = 5000 \left(1 + \frac{0.12}{2}\right)^{2 \times 2}$

Case 2: Quarterly Compounding

For quarterly compounding, the interest is compounded four times a year, so:

• $n = 4$
• $t = 2$ years

Substitute these values into the formula:

$A_{\text{quarterly}} = 5000 \left(1 + \frac{0.12}{4}\right)^{4 \times 2}$

Let me calculate both values now.The future value of ₹5,000 invested for two years at an annual interest rate of 12% is as follows:

1. Semi-annually compounded: ₹6,312.38
2. Quarterly compounded: ₹6,333.85

The difference arises because the interest compounds more frequently in the quarterly option.

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How would the future value change if the interest rate were increased to 15%?
2. What would be the impact if the investment period was extended to 5 years?
3. Can we calculate the effective annual rate (EAR) for both compounding periods?
4. How would monthly compounding affect the future value?
5. What is the difference between simple and compound interest in this context?

Tip: The more frequently interest is compounded, the higher the future value due to interest being added to the principal more often!