Question

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

Answer 1

Hint: The approach is quite formula based and uses basic concepts of compound interest. The very crucial step is to identify the variables from the question and after that put the variables into the given compound interest formula and get an answer. We know that compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.
The standard formula used for calculating the compound interest is shown below:
\[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]
Here, A = final amount
P = initial principal balance
r = interest rate
n = number of compounding a year
t = total number of years

Complete step-by-step answer:
In our question, we have
P = 125000, r = 12%, n = 2, t = $\left( 1+\dfrac{1}{2} \right)=\left( \dfrac{3}{2} \right)\text{years}$
If interest is compounded yearly then n = 1, if semiannually then n = 2, if quarterly then n = 4, monthly n = 12, weekly n = 52, daily n = 365.
In question, it is given half yearly (or semiannually) hence we have taken n = 2.
Now, we know, \[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]
By putting the values, we get:
\[\begin{align}
  & A=125000{{\left( 1+\dfrac{\left( \dfrac{12}{100} \right)}{2} \right)}^{2\times \dfrac{3}{2}}} \\
 & A=125000{{\left( 1+\dfrac{6}{100} \right)}^{3}} \\
 & A=125000{{\left( 1.06 \right)}^{3}} \\
 & A=148877 \\
\end{align}\]
Now, the amount of interest paid by Mr. Aslam is
\[\begin{align}
  & \Rightarrow \text{Interest} \\
 & \Rightarrow A-P \\
 & \Rightarrow 148877-125000 \\
 & \Rightarrow 23877 \\
\end{align}\]
Hence, Rs.23877 will be the final answer.

Note: The most common error made by students is that "writing value of A as their final answer". If students don't read the last line of the question properly then they will definitely give their answer as A. For finding the interest amount, we have to deduct our initial principal balance from the final amount A.
Second common error is the value of r. Students put the value of r as it is given in the question and don't divide by 100. In our question, r = 12 (wrong) but $r=\dfrac{12}{100}$ (right) in formula as it shows percentage.