p = 80000
r = 10%
t = 1.5 years

find the difference in the amount one would hv to pay if interest is :
- compounded annually
- compounded half yearly

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 (\(n = 1\))

\[
A_{\text{annual}} = 80000 \left(1 + \frac{0.10}{1}\right)^{1 \times 1.5}
= 80000 \times (1.10)^{1.5}
\]

### 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

Find the difference in the amount one would have to pay if interest is compounded annually and compounded half-yearly for a principal of ₹80,000 at an interest rate of 10% over 1.5 years.

Learn how to calculate the difference in amount for compound interest when compounded annually versus half-yearly for ₹80,000 at 10% interest over 1.5 years. Understand key mathematical concepts like compound interest formula, exponential growth, and how the number of compounding periods affects the final amount. Suitable for students in Grades 10-12.

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