Question

A sum of money under compound interest doubles itself in 4 years. In how many years will it become 16 times itself?

• A. 12
• B. 16
• C. 8
• D. 6

Answer 1

The correct option is B 16

When interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$
Given, $2P=P(1+\frac{R}{100}{)}^4$
$=>2=(1+\frac{R}{100}{)}^4$ --- (1)
And, $16P=P(1+\frac{R}{100}{)}^n$
$=>16=(1+\frac{R}{100}{)}^n$
$=>2^4=(1+\frac{R}{100}{)}^n$
From eqn 1
$=>\left(\right(1+\frac{R}{100}{)}^4{)}^4=(1+\frac{R}{100}{)}^n$
$=>(1+\frac{R}{100}{)}^{16}=(1+\frac{R}{100}{)}^n$
$=>n=16$