At which rate of simple interest does an amount become double in 12 ye

1.	At which rate of simple interest does an amount become double in 12 years?1. 8%2. \(8(\frac1 3)\)%3. \(7(\frac2 3)\)%4. \(8(\frac4 5)\)%
Answer» Correct Answer - Option 2 : \(8(\frac1 3)\)% Given: Amount becomes double in 12 years Formula Used: Simple Interest = (P × r × t)/100 Amount = P + Simple Interest Where P → Principal r → Rate of interest t → Time Calculation: Let principal be 100 Amount = P + Simple Interest ⇒ 2 × 100 = 100 + Simple Interest ⇒ Simple Interest = 100 Simple Interest = (P × r × t)/100 ⇒ 100 = (100 × r × 12)/100 ⇒ r = 100/12 ⇒ r = 25/3 \( \Rightarrow {\rm{r}} = 8\frac{1}{3}\;\% \) ∴ The rate of interest is \(8\frac{1}{3}\;\% .\)

At which rate of simple interest does an amount become double in 12 years?1. 8%2. \(8(\frac1 3)\)%3. \(7(\frac2 3)\)%4. \(8(\frac4 5)\)%

Answer» Correct Answer - Option 2 : \(8(\frac1 3)\)%

Given:

Amount becomes double in 12 years

Formula Used:

Simple Interest = (P × r × t)/100

Amount = P + Simple Interest

Where P → Principal

r → Rate of interest

t → Time

Calculation:

Let principal be 100

Amount = P + Simple Interest

⇒ 2 × 100 = 100 + Simple Interest

⇒ Simple Interest = 100

Simple Interest = (P × r × t)/100

⇒ 100 = (100 × r × 12)/100

⇒ r = 100/12

⇒ r = 25/3

\( \Rightarrow {\rm{r}} = 8\frac{1}{3}\;\% \)

∴ The rate of interest is \(8\frac{1}{3}\;\% .\)

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