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=(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`

`(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]`

`(\log2)/(\log(1.25))=n`

`n\approx 3.11`

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