# Find Out the Time

In what time Rs.8,000 will amount to Rs. 9,261 at 10% per annum compound interest, when the interest is compounded half yearly?

- 2 years
- 7/2 years
- 3/2 years
- 5/2 years

**Answer: (3) 3/2 years
**

**Explanation:-**

Let the time is N years

**Given-**

Principal = Rs.8000, Amount = Rs.9,261 & Rate = 10 %.

**Formula-**

**Compound Interest = P [(1 + R/100) ^{t} – 1]**

**Where, P = principal, R = rate, t = time.**

If interest is compounded half yearly then, the time is become double & rate is become half.

Then,

9261 = 8000 (1 + 10/2 x 100)

^{2N}

9261= 8000 (1 + 1/20)

^{2N }9261/8000 = (21/20)

^{2N }(21 x 21 x 21)/(20 x 20 x 20 ) = (21/20)

^{2N }(21/20)

^{3}= (21/20)

^{2N }Comparing on both side,

2 N = 3

N = 3/2 yearsHence, the answer is (3) 3/2 years.