Question

the difference between simple interest and compound interest of an amount at r% P.A after one year​

Answer 1

Answer:

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Answer 2

Given,

Interest rate = r% per annum,

Time = 1 year.

To find,

Difference between compound and simple interest for the given condition.

Solution,

We can solve this problem simply by following the below process.

Here, r% is given as the rate of interest on a principal amount (let P) for 1 year.

So, first, let's find out compound interest (CI). Assuming the interest is compounded annually, CI is given by,

$CI=P[(1+\frac{r}{100} )^t-1]$

Substituting given conditions,

$CI=P[(1+\frac{r}{100} )^1-1]\\CI=[P+\frac{Pr}{100}-P]\\CI=\frac{Pr}{100}$

Now, since simple interest (SI) is given by,

$SI=\frac{P\cdot r\cdot t}{100}$

For the given conditions, that is t = 1 year,

$SI=\frac{Pr}{100}$

Now, the difference between CI  and SI will be,

$CI-SI$

$=[\frac{Pr}{100} ]-[\frac{Pr}{100} ]$

$=0$

⇒ $CI-SI=0$

Therefore, after 1 year, for the same principal amount and rate of interest, the difference between compound interest and simple interest will be 0.