Question

In how many year the interest will became equal to the principal is rs.1200 is deposited at the rate of 25% in a bank ​

Answer 1

Given:

Principal = Rs. 1200

Rate of interest = 25%

To find:

The time in which the interest will became equal to the principal.

Solution:

We have,

$P=1200$

$r=\dfrac{25}{100}$

$r=0.25$

If interest is equal to the principal, then

$Amount=Principal+Interest$

$Amount=1200+1200$

$Amount=2400$

The formula for amount is:

$A=P\left(1+r)^n$

Substituting $A=2400, P=1200, r=0.25$ in the above formula, we get

$2400=1200(1+0.25)^n$

$\dfrac{2400}{1200}=(1.25)^n$

$2=(1.25)^n$

Taking log on both sides, we get

$\log2=\log(1.25)^n$

$\log2=n\log(1.25)$               $[\because \log a^b=b\log a]$

$\dfrac{\log2}{\log(1.25)}=n$

$n\approx 3.11$

Therefore, the interest will became equal to the principal in about 3.11 years.