Question
A certain sum amounts to Rs. 1800 in 3 years and to Rs. 2592 in 5 years, when invested at R% p.a. compound interest, compounded annually. Find the amount received when Rs. 3000 is invested at (R – 10)% p.a. simple interest for 4 years.
Solution
Let, the sum invested at compound interest be Rs. ‘P’ According to the question, {P(1 + R/100)⁵}/{P(1 + R/100)³} = 2592/1800 Or, (1 + R/100)² = 1.44 = (1 + 20/100)² Or, R = 20 Therefore, new rate of interest = 20 – 10 = 10% Required amount received at simple interest
= {(3000 × 10 × 4)/100} + 3000
= 1200 + 3000
= Rs. 4200
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