Question

In how many years, a certain sum becomes 4 times of itself at a rate of 15%?​

Answer 1

Answer:

The number of years required is 20.

Step-by-step explanation:

Let $x$ be the amount and we need to calculate the number of years it needs to reach 4 times the amount in the beginning when the rate of interest is 15%.

The formula to calculate the interest is

$I=\dfrac{PNR}{100}$

Where P is the principal amount, N is the number of years and R is the annual rate of interest. Also, the accumulated amount after N years is calculated using the formula,

$A=P(1+\frac{RN}{100})$

Here we need the accumulated amount to be $4x$. So we have

$4x=x(1+\frac{N\times 15}{100} )\\\\\implies \frac{4x}{x}= (1+\frac{N\times 15}{100} )\\\\\implies 4= (\frac{100+N\times 15}{100} )\\\\\implies 4\times 100=100+15N\\\\\implies 400=100+15N\\\\\implies 15N=400-100=300\\\\\implies N=\dfrac{300}{15}=20$

So it needs 20 years to reach the amount 4 times to itself.

Answer 2

Answer:

The number of years required is 20.

Step-by-step explanation:

Let  be the amount and we need to calculate the number of years it needs to reach 4 times the amount in the beginning when the rate of interest is 15%.

The formula to calculate the interest is

Where P is the principal amount, N is the number of years and R is the annual rate of interest. Also, the accumulated amount after N years is calculated using the formula,

Here we need the accumulated amount to be . So we have

So it needs 20 years to reach the amount 4 times to itself.