Question

Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is ${\text{Rs 125000}}$ and the Parishad charges interest at $12\% $ per annum compounded half-yearly. Find the interest paid by Aslam after a year and half.

Answer 1

Hint: Here we must know that when the principal amount which is here ${\text{Rs 125000}}$ is given to us at a specific rate then we can calculate the total amount at the end of $n{\text{ years}}$ being compounded half yearly is $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$ and here $r$ is the rate calculated per annum but for $n$ years. So we can subtract the value of principle from the amount to get the interest.

Complete Step by Step Solution:
Here we are given a person named Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is ${\text{Rs 125000}}$ and the Parishad charges interest at $12\% $ per annum compounded half-yearly. As it is compounded half yearly we can say that in one and a half years, three half years are there.
Hence $n = 3$
Rate per annum for $n{\text{ years}} = r = \dfrac{{12}}{2} = 6\% $
Principal amount is given as $P = {\text{Rs 125000}}$
Now we can apply the formula to find the amount of this given value at the end of one and a half year by:
$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
$A = {\text{Rs 125000}}{\left( {1 + \dfrac{6}{{100}}} \right)^3}$
${\text{A}} = {\text{Rs 125000}}{\left( {\dfrac{{106}}{{100}}} \right)^3} = {\text{Rs 125000}}{\left( {\dfrac{{53}}{{50}}} \right)^3}$
So on solving this further we get:
${\text{A}} = {\text{Rs 125000}}\left( {\dfrac{{\left( {53} \right)\left( {53} \right)\left( {53} \right)}}{{\left( {50} \right)\left( {50} \right)\left( {50} \right)}}} \right)$$ = {\text{Rs 148877}}$
So now we can subtract the value of principle from amount and get the value of compound interest which is required to us.
${\text{Interest}} = A - P = {\text{Rs }}\left( {148877 - 125000} \right) = {\text{Rs 23877}}$

Hence we get the value of compound interest as ${\text{Rs 23877}}$

Note:
Here we must know that when we are told to find the simple interest instead of compound we directly need to apply the formula of the simple interest which is given as ${\text{SI}} = \dfrac{{\left( P \right)\left( R \right)\left( T \right)}}{{100}}$ and therefore we must not confuse between the both.