A certain sum of money at compound interest turns 2 times itself in 9

1.	A certain sum of money at compound interest turns 2 times itself in 9 years. At the same rate of interest, in how many years will it become 32 times of itself?1. 35 years2. 25 years3. 45 years4. 15 years
Answer» Correct Answer - Option 3 : 45 years Given: A certain sum of money at compound interest turns 2 times itself in 9 years. Concept used: A = P(1 + R/100)T Where, A → Amount P → Principal R → Rate of interest T → Time Calculations: A = P(1 + R/100)T According to the question ⇒ 2P = P(1 + R/100)⁹ ⇒ 2 = (1 + R/100)⁹ ----(1) ⇒ 32P = P(1 + R/100)^T ⇒ 32 = (1 + R/100)^T ⇒ 2⁵ = (1 + R/100)^T From eq. (1) ⇒ {(1 + R/100)⁹}⁵ = (1 + R/100)^T ⇒ (1 + R/100)⁴⁵= (1 + R/100)^T ⇒ T = 45 years. ∴ The required time is 45 years

A certain sum of money at compound interest turns 2 times itself in 9 years. At the same rate of interest, in how many years will it become 32 times of itself?1. 35 years2. 25 years3. 45 years4. 15 years

Answer» Correct Answer - Option 3 : 45 years

Given:

A certain sum of money at compound interest turns 2 times itself in 9 years.

Concept used:

A = P(1 + R/100)T

Where,

A → Amount

P → Principal

R → Rate of interest

T → Time

Calculations:

A = P(1 + R/100)T

According to the question

⇒ 2P = P(1 + R/100)⁹

⇒ 2 = (1 + R/100)⁹ ----(1)

⇒ 32P = P(1 + R/100)^T

⇒ 32 = (1 + R/100)^T

⇒ 2⁵ = (1 + R/100)^T

From eq. (1)

⇒ {(1 + R/100)⁹}⁵ = (1 + R/100)^T

⇒ (1 + R/100)⁴⁵= (1 + R/100)^T

⇒ T = 45 years.

∴ The required time is 45 years

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