Question
Rohan deposited Rs. ‘Y’ in a bank offering compound
interest of 10% p.a. compounded annually. After 3 years, he invested the amount received from the bank in scheme ‘C’ and ‘D’ in the ratio of 7:3 respectively. Scheme ‘D’ offers compound interest of 18% p.a. compounded annually while scheme ‘C’ offers simple interest of 12% p.a. If total interest received by him from schemes C and D together at the end of 2 years is Rs. 1584, then find the value of ‘Y’.(Calculate approximate value)Solution
ATQ, Amount after 3 years at 10% CI = Y × (1.1)3 = Y × 1.331 Split into Scheme C and D (7:3): Scheme C = 1.331Y × 7/10 = 0.9317Y Scheme D = 1.331Y × 3/10 = 0.3993Y Interest from Scheme C (SI @12% for 2 yrs) = 0.9317Y × 12 × 2 / 100 = 0.2236Y Interest from Scheme D (CI @18% for 2 yrs) = 0.3993Y × [(1.18)^2 – 1] = 0.3993Y × 0.3924 = 0.1566Y Total Interest = 1584 0.2236Y + 0.1566Y = 1584 0.3802Y = 1584 Y = 1584 / 0.3802 = ₹4165.87 or approx ₹4165
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