Arun took a loan of Rs. 390625 from Kuber Finance. If the company charges interest at 16% per annum compounded quarterly, what amount will discharge his debt after one year?

Hint: Since, the interest is compounded quarterly, determine the rate of interest for one quarter and total quarters for the given time. Then substitute these values in the formula of compound interest, $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$ and then simplify it to get the amount that Arun will have to give to get discharge from his debt.

Complete step-by-step answer:
We are given that the company charges 16% interest per annum compounded quarterly and the amount of money that Arun took is Rs. 390625.
If 16% is the interest of 1 year, then the interest of one quarter can be calculated by dividing it by 4.
Then, the interest for one quarter is \[\dfrac{{16}}{4} = 4\% \]
Also, there are 4 quarters in a year, so time will be taken as 4.
We know that amount on a principal amount $P$ at an interest of $r\% $ and time $t$ years when interest is compounded annually is given by $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$
Now substitute 390625 for $P$ , 4 for \[r\] and 4 for $t$ in the above formula.
$A = 390625{\left( {1 + \dfrac{4}{{100}}} \right)^4}$
On simplifying the expression, we will get,
$
  A = 390625{\left( {1.04} \right)^4} \\
   \Rightarrow A = 456976 \\
$
Thus, the amount that will discharge Arun's debt is Rs. 456976.

Note: When we have to calculate the compound interest quarterly and the rate of interest is given annually, then we divide the rate of interest by 4 and multiply the given time by 4. In this interest after every quarter gets added to the principal amount of the next quarter.