Question

The integral number of years in which a sum of money at 25% p.a. under compound interest will become more than twice itself, is at least.

• A. 3
• B. 2
• C. 4
• D. 1

Answer 1

The correct option is C 4

When interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$
Given, $Amount\ge 2P$
$=>P(1+\frac{25}{100}{)}^n\ge 2P$
$=>(1.25{)}^n\ge 2$
When, $n=2$
$A=1.25\times 1.25=1.5625$ which is not greater than or equal to $2$
When, $n=3$
$A=1.25\times 1.25\times 1.25=1.953125$ which is not greater than or equal to $2$
When, $n=4$
$A=1.25\times 1.25\times 1.25\times 1.25=2.44140625$ which is greater than $2$
So, number of years should be atleast $4$