# In how many years ₹ 1000 will become ₹ 1331 at the rate of 20% per annum if the interest is compounded semi-annually?

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In how many years ₹ 1000 will become ₹ 1331 at the rate of 20% per annum if the interest is compounded semi-annually?
1. 1/2 years
2. 2 years
3. 3 years
4. 3/2 years

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Correct Answer - Option 4 : 3/2 years

Given:

Principal = ₹ 1000

Amount = ₹ 1331

Rate = 20%

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:

Let the original time be t years

New rate = 20%/2 = 10%

New time = 2 × t = 2t years

₹ 1331 = ₹ 1000[1 + 10/100]2t

⇒ ₹ 1331/₹ 1000 = [1 + 1/10]2t

⇒ 1331/1000 = [11/10]2t

⇒ (11/10)3 = [11/10]2t

Comparing the powers because the bases are same

⇒ 2t = 3

⇒ t = 3/2

∴ In 3/2 years ₹ 1000 will become ₹ 1331 at the rate of 20% per annum if the interest is compounded semi-annually