Question

A sum becomes 5 times of itself in 3 years. at compound interest (interest is compounded annually). In how many years. will the sum becomes 125 times of itself?

• A. 9
• B. 6
• C. 8
• D. 12

Answer 1

Answer:

A. 9

Solution: Given: A sum becomes 5 times of itself in 3 years. at compound interest (interest is compounded annually). Formula Used: When calculate at compound interest Amount (A) = p (1 + r/100)n Where p, r, and n respectively are principal, rate of interest, and time Calculation: Let the sum be p Rate be r% According to the question, 5p = p(1 + r/100)3 ⇒ 5 = (1 + r/100)3 ...i) Let the sum becomes 125 times in n years. 125p = p(1 + r/100)n ⇒ 125 = (1 + r/100)n ⇒ (5)3 = (1 + r/100)n ...ii) Comparing equation (ii) with (i) we get, n = 9 ∴ In 9 years it will become 125 times. Alternate Method: A certain sum at C.I becomes ‘y’ times in n1 years. and ‘z’ times in n2 years. then y1/n1 = z1/n2 Using the above formulae, we have ⇒ 51/3 = 1251/n2 ⇒ 51/3 = 53/n2 ⇒ n2 = 9 years. ∴ The sum becomes 125 times of itself in 9 years.