To find the difference in the amount payable when interest is compounded annually and compounded half-yearly, we will use the compound interest formula:

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

Where:

• $A$ is the amount after interest.
• $P$ is the principal amount (₹80,000).
• $r$ is the annual interest rate (10% or 0.10).
• $n$ is the number of times interest is compounded per year.
• $t$ is the time in years (1.5 years).

Case 1: Compounded Annually ($n = 1$)

= 80000 \times (1.10)^{1.5}$$ ### Case 2: Compounded Half-Yearly ($$n = 2$$) $$A_{\text{half-yearly}} = 80000 \left(1 + \frac{0.10}{2}\right)^{2 \times 1.5} = 80000 \times \left(1 + 0.05\right)^{3}$$ Now, let’s compute both amounts and find the difference.### Results: 1. Amount when compounded annually: ₹92,295.18 2. Amount when compounded half-yearly: ₹92,610.00 3. Difference in the amounts: ₹314.82 Thus, the amount payable with half-yearly compounding is ₹314.82 more than with annual compounding. Do you want further details or explanations? Here are 5 related questions: 1. How would the difference change if the time period were extended to 3 years? 2. What happens to the interest difference if the rate is increased to 12%? 3. How would quarterly compounding affect the payable amount? 4. Can you calculate the total interest earned in both cases? 5. What would the principal be if the final amount after 1.5 years