# Find the compound interest on ₹ 8000 at the rate of 10% per annum for 3/2 years if the interest is compounded semi-annually?

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Find the compound interest on ₹ 8000 at the rate of 10% per annum for 3/2 years if the interest is compounded semi-annually?
1. ₹ 1240
2. ₹ 1200
3. ₹ 1261
4. ₹ 1241

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Correct Answer - Option 3 : ₹ 1261

Given:

Principal = ₹ 8000

Rate = 10%

Time = 3/2 years

Interest is compounded semi-annually

Concept Used:

If interest is compounded semi-annually means interest is calculated in every six month that is 2 times in a year or we can simply convert this problem in normal compound interest problem by multiplying the time by 2 and dividing the rate by 2

Formula Used:

Amount = Principal[1 + (Rate/100)]Time

Amount = Principal + Interest

Calculation:

New rate = 10%/2 = 5%

New time = 3/2 × 2 = 3 years

Amount = ₹ 8000[1 + 5/100]3

⇒ Amount = ₹ 8000[1 + 1/20]3

⇒ Amount = ₹ 8000[21/20]3

⇒ Amount = ₹ 8000[9261/8000]

⇒ Principal + Interest = ₹ 9261

⇒ Interest = ₹ 9261 – ₹ 8000

⇒ Interest = ₹ 1261

∴ The compound interest on ₹ 8000 at the rate of 10% per annum for 3/2 years if the interest is compounded semi-annually is ₹ 1261