Question
A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?
Answer: Option D
Answer: (d)Let the principal be Rs.1.A = P$(1 + R/100)^T$8 = 1$(1 + R/100)^3$$2^3 = 1(1 + R/100)^3$2 = 1$(1 + R/100)^1$$2^4 = (1 + R/100)^4$Time = 4 yearsUsing Rule 11,Here, $x = 8, n_1 = 3, y = 16, n_2$ = ?Using $x^{1/n_1} = y^{1/n_2}$$(8)^{1/3} = (16)^{1/n_2}$$(2^3)^{1/3} = (2^4)^{1/n_2}$$2^1 = 2^{4/n_2}$1= $4/n_2$$n_2$ = 4 years
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Answer: (d)Let the principal be Rs.1.A = P$(1 + R/100)^T$8 = 1$(1 + R/100)^3$$2^3 = 1(1 + R/100)^3$2 = 1$(1 + R/100)^1$$2^4 = (1 + R/100)^4$Time = 4 yearsUsing Rule 11,Here, $x = 8, n_1 = 3, y = 16, n_2$ = ?Using $x^{1/n_1} = y^{1/n_2}$$(8)^{1/3} = (16)^{1/n_2}$$(2^3)^{1/3} = (2^4)^{1/n_2}$$2^1 = 2^{4/n_2}$1= $4/n_2$$n_2$ = 4 years
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