Question

Rohit deposited Rs. 10,000 in a bank for six months. If the bank pays the compound interest at \[12\% \] per annum reckoned quarterly, find the amount to be received by him on maturity.

Answer 1

Hint:Here we use the formula of compound interest to calculate the value of the amount Rohit receives. We convert the time period from months to years into quarters and we convert the rate of interest from per annum to rate of interest per quarter.

Formula used:If amount from compound interest is denoted by A, Principal amount by P, Rate of interest by R and time period by T, then we have the formula \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\].

Complete step-by-step answer:
We know that the principal amount given is Rs. 10,000.
So, \[P = 10000\]
Bank pays \[12\% \] compound interest per annum second quarterly.
When we have compound interest per annum, then we write the rate of interest same as given to us, but here we convert the rate of interest from per annum to per quarter by multiplying the rate of interest by \[\dfrac{1}{4}\].
Rate of interest for 1 year is \[12\% \]
So rate of interest for \[\dfrac{1}{4}\]of a year is given by \[\dfrac{1}{4} \times 12\% \]
Calculate the value of Rate of interest.
Therefore, \[R = 3\% \]
Also, the time period is 6 months.
We convert the time period from months to quarters by first converting the time period from months to years and then dividing by \[\dfrac{1}{4}\].
We know 12 months give us 1 year
Using unitary method, we can write
\[ \Rightarrow \]1 month is \[\dfrac{1}{{12}}\]of a year.
\[ \Rightarrow \]6 months will be \[\dfrac{1}{{12}} \times 6\] of the year.
\[ \Rightarrow \]6 months is \[\dfrac{1}{2}\]year.
Now we know 1 year has 4 quarters.
So, using unitary method again, we can write
\[ \Rightarrow \]year has quarters.\[\dfrac{1}{2}\]
Calculate the value of time period.
So, time period becomes \[T = 2\]
We know \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]
Now we substitute the values of \[P = 10000,R = 3,T = 2\]in the formula for compound interest.
 \[ \Rightarrow C = 10000{\left( {1 + \dfrac{3}{{100}}} \right)^2}\]
Take LCM inside the bracket
\[ \Rightarrow A = 10000{\left( {\dfrac{{100 + 3}}{{100}}} \right)^2}\]
\[ \Rightarrow A = 10000{\left( {\dfrac{{103}}{{100}}} \right)^2}\]
Now square the terms inside the bracket.
\[ \Rightarrow A = 10000\dfrac{{103 \times 103}}{{100 \times 100}}\]
Cancel the same terms from numerator and denominator.
\[ \Rightarrow A = 10609\]
Thus, the amount received by him on maturity is Rs. 10609.

Note:Students are likely to make mistakes in the solution because they don’t convert the values of time period and rate of interest given in terms of years to quarterly. Keep in mind to always convert the terms according to the need of the question and then substitute values in the formula.