Question

Arun took a loan of Rs. 390625 from Kuber finance. If the company charges interest at 16% per annum, compound quarterly, what amount will charge his debit after one year?

Answer 1

Hint: In this question, from the given rate of interest per annum we need to find we need to find the amount for the given principal using the formula for the interest if compounded quarterly which is given by\[A=P{{\left( 1+\dfrac{\dfrac{R}{4}}{100} \right)}^{4T}}\]. Now, we can find the compound interest by using the formula given by \[CI=A-P\]. Then on further simplification we get the result.

Complete step-by-step answer:
If R is the rate of interest per annum, T is the duration in years, A is the amount and P is the principal
If interest is compounded quarterly, then
\[A=P{{\left( 1+\dfrac{\dfrac{R}{4}}{100} \right)}^{4T}}\]
Now, from the given respective values in the question we have
\[P=390625,R=16,T=1\]
Now, from the above formula we have
\[\Rightarrow A=P{{\left( 1+\dfrac{\dfrac{R}{4}}{100} \right)}^{4T}}\]
Now, on further substituting the respective values we get,
\[\Rightarrow A=390625{{\left( 1+\dfrac{\dfrac{16}{4}}{100} \right)}^{4\times 1}}\]
Now, this can be further written in the simplified form as
\[\Rightarrow A=390625{{\left( 1+\dfrac{4}{100} \right)}^{4}}\]
Now, this can be further written in the simplified form
\[\Rightarrow A=390625{{\left( \dfrac{26}{25} \right)}^{4}}\]
Now, on further simplification we get,
\[\therefore A=Rs.456976\]
Now, the relation between compound interest, amount and principal is given by the formula
\[\Rightarrow CI=A-P\]
Now, on substituting the respective values we get,
\[\Rightarrow CI=456976-390625\]
Now, on further simplification we get,
\[\therefore CI=Rs.66351\]

Note: Instead of directly using the formula for amount when compounded quarterly we can also solve it by usual compounded annual formula by taking the rate of interest will be quarter of the given rate of interest and the time of interest will also be quarter which on further simplification gives the same result.It is important to note that the amount calculated will include the compound interest and principal as we know from the definition of compound interest that if the interest is not paid at the end of the year then it gets added to the principal.