Find the compound interest on ₹5,70,000 for 1.5 years at 10% per annum compounded half-yearly.
₹89,846.25
To find the compound interest on ₹5,70,000 for 1.5 years at an interest rate of 10% per annum compounded half-yearly, we can use the formula for compound interest:
\(A = P \left(1 + \frac{r/n}{100}\right)^{nt}\)
where:
- A is the amount after time t.
- P is the principal amount (₹5,70,000).
- r is the annual interest rate (10%).
- n is the number of times interest applied per time period (2 for half-yearly).
- t is the time the money is invested for in years (1.5 years).
First, convert the time period into the number of compounding periods:
\(t = 1.5 \ \text{years} = 3 \ \text{half-year periods}\)
Calculate the compound amount using the provided values:
\(A = 570000 \left(1 + \frac{10/2}{100}\right)^{3}\)
\(A = 570000 \left(1 + 0.05\right)^{3}\)
\(A = 570000 (1.05)^{3}\)
Now compute \((1.05)^3\):
\((1.05)^3 = 1.157625\)
Therefore, the amount \(A\) is:
\(A = 570000 \times 1.157625 = 659846.25\)
The compound interest is given by:
\(CI = A - P = 659846.25 - 570000 = 89846.25\)
Thus, the compound interest after 1.5 years is ₹89,846.25.
The correct answer is ₹89,846.25.
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