1.

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 ?1). 6 years2). 4 years3). 8 years4). 5 years

Answer»

Formula for compound INTEREST:-

$(A = P{\left( {1 + \FRAC{R}{{100}}} \right)^T})$, CI = A – P

Where CI is compound interest, A is amount, P is principal, R is rate, T is time

Given, Sum of money BECOMES 8 times in 3 years.

∴ A = 8P

$(\Rightarrow 8{\rm{P}} = P{\left( {1 + \frac{R}{{100}}} \right)^3})$

$(\Rightarrow {\rm{\;}}8 = {\left( {1 + \frac{R}{{100}}} \right)^3})$

$(\Rightarrow {2^3} = {\left( {1 + \frac{R}{{100}}} \right)^3})$

⇒ 2 = 1 + R/100

⇒ R = 100 %

Let the time be T in which sum of money becomes 16 times of itself.

∴ A = 16P

$(\Rightarrow 16{\rm{P\;}} = P{\left( {1 + \frac{R}{{100}}} \right)^T})$

$(\Rightarrow 16{\rm{\;}} = {\left( {1 + \frac{{100}}{{100}}} \right)^T})$

⇒ 24 = 2T

By property of indices ; ab = ac, ⇒ b = c

⇒ T = 4 years


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