The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, t is the time in years, and n is the number of times the interest is compounded per year.
In this case, P = ₹10000, r = 20%, t = 2 years, and n = 2 (compounded half-yearly).
So, A = 10000(1 + 0.20/2)^(2*2) = ₹14864.10
The compound interest is A - P = ₹14864.10 - ₹10000 = ₹4864.10
Therefore, the compound interest on ₹10000 for 2 years at 20% per annum compounded half yearly is ₹4864.10.
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Answer:
The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the rate of interest, t is the time in years, and n is the number of times the interest is compounded per year.
In this case, P = ₹10000, r = 20%, t = 2 years, and n = 2 (compounded half-yearly).
So, A = 10000(1 + 0.20/2)^(2*2) = ₹14864.10
The compound interest is A - P = ₹14864.10 - ₹10000 = ₹4864.10
Therefore, the compound interest on ₹10000 for 2 years at 20% per annum compounded half yearly is ₹4864.10.
Verified answer
Solution :
Given, principal, P = ₹10,000
Time, n = 2 years.
Rate of interest, r = 20% per annum compounded half yearly.
To find : Compound interest.
We know formula for compound interest compounded half yearly :
→ CI = P(1 + r/200)²ⁿ - P
Substituting values,
→ CI = 10000(1 + 20/200)^(2 × 2) - 10000
→ CI = 10000(1 + 0.1)⁴ - 10000
→ CI = 10000(1.1)⁴ - 10000
→ CI = 14641 - 10000
→ CI = ₹4641
Therefore,
Compound interest = ₹4641.