Question

What will Rs \[125000\] amount to at the rate of \[6\% \], if the interest is calculated after every four months?

Answer 1

Hint: We will first calculate the rate for four months. Since, four months is equal to one-third of a year, so to get the rate for four months we will divide the given rate by three. Then we will find the time by dividing \[12\] months by \[4\] months. Then, we will put these details in the formula for calculating the amount.
Formula used:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]
\[A = {\text{ amount}}\]
\[P = {\text{ principal amount}}\]
\[R = {\text{ rate}}\]
\[n = {\text{ time - period}}\]

Complete step by step answer:
Given;
\[P = 125000\]
\[R = 6\% \] per annum
Total time \[ = 1\] year
Now as interest is compounded after every four months, so to find the interest rate for four months we will divide the given rate by \[3\]. So,
\[R = \left( {\dfrac{6}{3}} \right)\% \]
\[ \Rightarrow R = 2\% \] per four months
Now, to calculate \[n\] we will divide total time that is \[12\] months by \[4\], because interest is compounded after every \[4\] months.
\[ \Rightarrow n = \dfrac{{12}}{4}\]
\[ \Rightarrow n = 3\]

Now we will use the formula for calculating the amount. We know,

\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}\]
Now, we will put the values of \[P,R,n\] in this equation. So, we get
\[ \Rightarrow A = 125000{\left( {1 + \dfrac{2}{{100}}} \right)^3}\]
Now taking the LCM and solving the terms in the bracket we get:
\[ \Rightarrow A = 125000{\left( {\dfrac{{102}}{{100}}} \right)^3}\]
On further simplification we get,
\[ \Rightarrow A = 125000 \times 1.061208\]
\[ \Rightarrow A = 132651\]
So, the amount is Rs \[1,32,651\].

Note:
One major mistake that students make is that they take the rate to be \[6\% \] in the formula for calculating the amount. But we cannot take the rate to be equal to \[6\% \] because it is for a year and in the question, it is given that the rate is calculated after every four months. Another point to note is that we can also solve this question by calculating the simple interest after four months and adding the interest to the principal amount and then we will calculate the interest for next four months on that total amount and similarly for the last four months.