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?

  1. 2 years
  2. 7/2 years
  3. 3/2 years
  4. 5/2 years
Desire Adnan Default Asked on 5th August 2015 in Maths.
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1 Answer(s)

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.

Anurag Mishra Professor Answered on 5th August 2015.
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