Question

At what rate per cent per annum will a sum double itself in 5

years if interest is simple

(A) 25% (B) 20% (C) 10% (D) 12.5%​

Answer 1

Given :-

• Time = 5 years
• Principal doubles itself in the time period
• Simple interest is levied

To find :-

• Rate %

Formula to use :-

$rate \: = \dfrac{simple \: interest \times 100}{principal \times time}$

Let rate be y and principal be ₹x

If amount becomes double,

Amount = 2 × x = ₹2x

Simple interest = Amount - Principal

Substituting the values,

Simple interest = 2x - x

Simple interest = ₹x

By applying the formula,

$y = \dfrac{x \times 100}{x \times 5}$

$y= \dfrac{100x}{5x}$

By reducing to the lowest terms,

$y = 20\%$

Hence at 20% per annum, Simple Interest levied, the principal will become double after 5 years.

Correct option = option (b) 20%

Important points to note :-

• Amount = Simple Interest + Principal
• Simple interest = Amount - Principal
• Principal = Amount - Simple Interest

Some more formulas :-

$simple \: interest \: = \dfrac{principal \times \: rate \times \: time}{100}$

$principal = \dfrac{simple \: interest \times 100}{time \times \: rate}$

$time \: = \dfrac{ simple \: interest \: \times 100}{principal \times rate}$