Question

A finance company declares that, at a certain 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 will it become 16 times ?

Answer 1

Answer:

For the sum to become 16 times it takes 4 years

Step-by-step explanation:

Compound Interest = P(1+R)^N

Where

P = principle

R = rate of interest

N = number of years

sum of money deposited by anyone will become 8 times in three years

P(1+R)^3 = 8P

1+R = 2

R=1%

in how many years will it become 16 times at same compound interest  ?

P(1+1)^N = 16P

2 ^N =16

N = 4 years

Answer 2

4 years it will become 16 times  

Given:

Amount of money deposited will become 8 times in three years.

Simple interest, SI = 8P ; P is amount of money deposited (Principle Amount)

To find:

In how many years, the amount will become 16 times = ?

Solution:

Let the amount of money deposited be ‘P’

We know that Simple Interest,

$S I=P\left(1+\frac{R}{100}\right)^{n}$

where R is the rate of interest and n is the number of years  

Then,  

$\begin{array}{l}{8 P=P\left(1+\frac{R}{100}\right)^{3}} \\ {\Rightarrow 8=\left(1+\frac{R}{100}\right)^{3}} \\ {\Rightarrow\left(1+\frac{R}{100}\right)^{3}=2^{3}}\end{array}$

$\Rightarrow 1+\frac{R}{100}=2 \ldots \ldots .(1)$

We need to find the number of years where the amount will become 16 times.

So,  

$\begin{array}{l}{16 P=P\left(1+\frac{R}{100}\right)^{n}} \\ {\Rightarrow 16=\left(1+\frac{R}{100}\right)^{n}} \\ {\Longrightarrow 2^{n}=16(\text { from } 1)} \\ {\Rightarrow 2^{n}=2^{4}}\end{array}$

$\Rightarrow n=4$

Therefore, in 4 years, the amount becomes 16 times.