Question

Sangeeta lent Rs.40,960 to Amar to purchase a shop at $12\% $ per annum. If the interest is compounded semi-annually, find the interest paid by Amar after $1\dfrac{1}{2}$ years.

Answer 1

Hint: Here, in this question, we have the principal, rate, and the time so by using all these we will first calculate the compound interest by using the formula, $A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}$ and then after solving it to calculate the interest we will take the difference of CI and the principal.

Formula used:
Compound interest,
$A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}$
$A$ , will be the final amount
$P$ , will be the principal
$r$ , will be the rate of interest
$t$ , will be the time periods
$n$ , will be the number of interests being applied.

Complete step-by-step answer:
Since, in the question, it is given that we have principal $Rs.40,960$ and the rate of interest is $12\% $ also the time semiannually so it is given as $\dfrac{3}{2}$ years.
So now firstly we will calculate the compound interest, so by using the formula and substituting the values, we get
$ \Rightarrow A = 40,960{\left( {1 + \dfrac{{12.5}}{{2 \times 100}}} \right)^{2 \times \dfrac{3}{2}}}$
And on solving the above equation, we get the equation as
$ \Rightarrow A = Rs.49,130$
Now we will calculate the interest, so for this, we will find out the difference between the compound interest and the principal of it. So on substituting the values, we get
$ \Rightarrow Rs.49,130 - Rs.40,960$
And on solving the above equation, we get the equation as
$ \Rightarrow Rs.8,170$
Therefore, the interest will be $Rs.8,170$ .

Note: For solving such a question we just need the formula and then we can easily get to the answer. The only thing is we should know when to calculate and which formula can lead to me. We should also know the basics about it. So the SI is calculated by using the principal, time and the CI will be calculated by using cumulative interest over the years.