Question

Find the compound interest on Rs. 4000 at the rate of 24% per annum for 3 months compounded monthly.

Answer 1

Hint: In this particular question use the concept that the compound interest is calculated as, C.I = A – P, where P = principal amount and A = amount after compound interest, so A is calculated as, $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$, where r is the rate of interest in percentage, n is the time in years, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
Principal amount = 4000 Rs.
Rate of interest, r = 24% per annum.
For 3 months compounded monthly.
I.e. ($\dfrac{3}{{12}}$) years compounded annually.
Therefore, $n = \dfrac{3}{{12}}$ Years.
Now as we know that the compound interest is calculated as, C.I = A – P, where P = principal amount and A = amount after compound interest, so A is calculated as, $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$, where r is the rate of interest in percentage, n is the time in years.
So, $A = 4000{\left( {1 + \dfrac{{24}}{{100}}} \right)^{\dfrac{3}{{12}}}}$
Now as we see that the power is in fraction, so we convert this power into integer by multiplying 12 and for this we have to divide the rate of interest by 12, so that overall no change.
I.e. n = $\dfrac{3}{{12}}$ years.=0.25
And r = $\dfrac{{24}}{{12}}$ = 2%
So that what he got at 24% interest per annum for 3 months compounded monthly, is same as he got at 2% interest per annum for 3 years compounded annually.
$ \Rightarrow A = 4000{\left( {1 + \dfrac{2}{{100}}} \right)^{0.25}}$
Now simplify this we have,
$ \Rightarrow A = 4000{\left( {\dfrac{{102}}{{100}}} \right)^(0.25)}$
$ \Rightarrow A = 4000\left( {\dfrac{{102}}{{100}} \times \dfrac{{102}}{{100}} \times \dfrac{{102}}{{100}}} \right)$
$ \Rightarrow A = 4\left( {\dfrac{{102}}{1} \times \dfrac{{102}}{{10}} \times \dfrac{{102}}{{100}}} \right) = 4\left( {\dfrac{{1061208}}{{1000}}} \right) = 4244.832$ Rs.
So the compound interest is, C.I = A – P = 4244.832 – 4000 = 244.832 Rs.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is the formula of compound interest which is stated above, so, first change 3 months compounded monthly to 3 months compounded yearly, then convert the fraction into integer by multiply by 12 and divide the interest by that same number so that overall no change now apply the formula as above and simplify we will get the required answer.