Question
Investor V placed Rs. (a + 3000) in a compound interest
account with an annual interest rate of r%, compounded annually for a span of 2 years. Simultaneously, investor T invested Rs. (a β 2000) in a simple interest account with an interest rate of (r β 2)% p.a. for a duration of 3 years. The cumulative interest earned by both investors amounted to Rs. 12360. Additionally, investor A contributed Rs. (a + 8000) in a simple interest account with a 15% interest rate for 3 years, accumulating an interest of Rs. 13500. The enigma to unravel is the value of 'r'.Solution
According to the question, Simple interest received by A = Rs. 13500 (a + 8000) Γ 15% Γ 3 = 13500 (a + 8000) = 30000 a = 22000 Amount invested by V = Rs. 22000 + 3000 = Rs. 25000 Amount invested by T = 22000 β 2000 = Rs. 20000 The total interest received by V and T = Rs. 12360 [25000 Γ (1 + r/100)2 β 25000] + [20000 Γ (r β 2)% Γ 3] = 12360 25000 Γ (1 + r/100)2 β 25000 + 600(r β 2) = 12360 25000 Γ (1 + r2/10000 + r/50) β 25000 + 600(r β 2) = 12360 25000 + 2.5r2 + 500r β 25000 + 600(r β 2) = 12360 2.5r2 + 500r + 600r β 1200 = 12360 2.5r2 + 1100r = 13560 r2 + 440r β 5424 = 0 r2 + 452r β 12r β 5424 = 0 r(r + 452) β 12(r + 452) = 0 (r + 452)(r β 12) = 0 r = -452, 12 Rate of interest cannot be negative. So, r = 12
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