A woman invested Rs. 75,000 at compound interest of 12%

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