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