Question
A certain amount is split equally between two investment
plans. One offers simple interest and the other compound interest, both at the same annual rate compounded yearly. After 2 years, the simple interest earned is Rs. 640, and the compound interest is Rs. 688. Find the rate of interest per annum.Solution
ATQ,
Let the amount invested in each scheme be Rs. 'P'. Let the annual interest rate be 'r%' p.a. Simple interest for 2 years = Rs. 640 So, SI per year = 640 ÷ 2 = Rs. 320 Since both interests match in the first year, CI for 1st year = Rs. 320 CI in 2nd year = 688 - 320 = Rs. 368 Now, this extra Rs. 48 is the interest on Rs. 320 for 1 year. 320 × r × 1 / 100 = 368 - 320 = 48 ⇒ r = (48 × 100) ÷ 320 = 15% Hence, Rate of Interest = 15%
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