Question
A woman invested Rs. 75,000 at compound interest of 12%
p.a. compounded annually for 1 year. If the interest had been compounded semi-annually, how much extra interest would she have earned?Solution
ATQ,
Amount = Principal X {1 + (rate/100)}ᵀᶦᵐᵉ ᴾᵉʳᶦᵒᵈ
So, compound interest = Amount - Principal
When compounded annually:
Amount at the end of one year = 75000 X {1 + (12/100)}¹ = Rs. 84,000
Interest earned = 84000 - 75000 = Rs. 9,000
When compounding semi-annually:
Effective rate = 12 ÷ 2 = 6%
Effective time = (12/12) X 2 = 2 periods
Amount = 75000 X {1 + (6/100)}² = Rs. 84,645
Interest = 84645 - 75000 = Rs. 9,645
Required difference = 9645 - 9000 = Rs. 645
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