# A sum of money was lent for 2 yrs @20%pa. componded anually. If the intrest is payable half yearly insted of yearly, than the intrest is rs482 more. find the sum..As got solution but still doubt---that why we have substacted amt from 1..

1
by singhgurpreet9

2014-10-16T14:35:53+05:30

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Let the sum be P.

Let the interest be compounded annually.
Accumulated total = S1 = P (1 + 20/100)² = P 1.2² = 1.44 P

Interest I1 = accumulated sum - Principal  = S1 -  P
= 1.44 P -  P = (1.44 - 1) P =   0.44 P

If the interest is compounded half-yearly, then:
interest for 6 months = 20% * 6/12 = 10%
number of times it is compounded is 4.

S2 = P ( 1 + 10/100)⁴ = P 1,1⁴ = 1.4641 P
Interest I2 = accumulated sum - Principal  = S2 -  P
= 1.4641 P - P  = (1.4641 - 1) P =  0.4641 P

Difference in the interest = S2 - S1 = I2 - I1 = 0.4641 P - 0.44 P

0.0241 P = Rs 482

P = Sum lent = Rs 20,000.
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Shorter method:        It is not necessary to compute Interests separately.  Difference in the accumulated sums also gives difference between interests.

Accumulated sum in case of compounding every 1 year
=
P (1 + 20/100)² = P 1.2² = 1.44 P

Accumulated sum in case of compounding every 6 months
= P (1 + 10/100)⁴ = P 1.1⁴ = 1.4641 P

So  difference = 0.0241 P = Rs 482
P = Rs 20,000

Answer by Jainsunny755 is exact copy; letter by letter, symbol by symbol; of your very nice explanation. Can you find ways to discourage persons to avoid such useless exercise. It will aslo lessen burden on resources of the site. May I request please to tell all to give second answer only if there is really different or better way to do so.
you are correct. I wish all persons know it and realize it.