The problem reads:

Madhu borrowed a sum of ₹24,000 for 2 years at the rate of 10% p.a., interest compounded annually. Find how much money will she have to pay to clear her debt?

This is a problem involving compound interest, and the formula to calculate the total amount $A$ (which includes the principal and the interest) is:

$A = P \left( 1 + \frac{r}{100} \right)^t$

Where:

• $P$ is the principal (the initial amount borrowed) = ₹24,000
• $r$ is the rate of interest per annum = 10%
• $t$ is the time in years = 2 years
• $A$ is the total amount after $t$ years, which we need to find.

Step-by-step solution:

1. Plugging in the values into the formula: $A = 24000 \left( 1 + \frac{10}{100} \right)^2$

2. Simplify inside the parentheses: $A = 24000 \left( 1 + 0.10 \right)^2 = 24000 \left( 1.10 \right)^2$

3. Calculate $(1.10)^2$: $1.10^2 = 1.21$

4. Now multiply by the principal: $A = 24000 \times 1.21 = 29,040$

Final Answer:

Madhu will have to pay ₹29,040 to clear her debt.

Would you like more details on any step or have any questions? Here are five related questions for practice:

1. What would be the total amount if the rate of interest were 8% instead of 10%?
2. How much interest would Madhu pay in total on this loan?
3. If the interest were compounded semi-annually, what would be the total amount after 2 years?
4. What is the compound interest earned after 2 years at 10% p.a.?
5. How would the amount change if the loan period were extended to 3 years at the same interest rate?

Tip: In compound interest, the interest earned in each period is added to the principal for the calculation of interest in the next period, unlike simple interest, where interest is calculated only on the initial principal.