Question

A finance company declares that, with compound interest rate, a sum of money deposited by anyone will become $8$ times in three years. if the same amount is deposited at the same compound-rate of interest, then in how many years it will become $16$ times?

• A. $8$ yrs
• B. $10$ yrs
• C. $4$ yrs
• D. $6$ yrs

Answer 1

The correct option is C $4$ yrs

Let the prnicipal $=x$ in Rs.

In the first case Time$=3$ yrs, amount $=8x$, rate $=R$.

Now Amount $=$ Principal $\times {(1+rate)}^{time}$

$\therefore x{(1+\frac{R}{100})}^3=8x⟹{(1+\frac{R}{100})}^3=2^3⟹1+\frac{R}{100}=2⟹R=100p.c.$

In the second case the amount $=16x$, Time $=n$.

$\therefore x{(1+\frac{100}{100})}^n=16x\Rightarrow {\left(2\right)}^n=2^4\Rightarrow n=4$ yrs

So, after $4$ years, the amount will become $16$ times of the invested money.