Question
Raj and Simran each invested a sum of ₹10,000 for
three years at 25% compound interest per annum. However, while for Raj the interest was compounded annually, for Simran it was compounded every six months. How much more will Simran receive as interest compared to Raj at the end of the three years?Solution
For Raj (compounded annually): Rate = 25% Time = 3 years A = ₹10,000 (1 + 25/100)3 = 10,000 × (5/4)3 = ₹19,531.25 Interest = A – P =19,531.25-10000 = ₹9,531.25 For Simran (compounded semi-annually): Rate for six months = 25 × 6/12 = 12.5% Time for Simran = 3 × 2 = 6 periods - A = ₹10,000 (1 + 12.5/100) 6 = 10,000 × (9/8)6 = ₹19,987.37 Interest = A – P =19987.37-10000 = ₹9,987.37 Difference in interest = ₹9,987.37 - ₹9,531.25 = ₹456
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