Question

Mrs. Gupta deposited Rs. 10000 in a bank for 5 years at a rate of 1.5% per month. How much money did she get at the end of that period?

Answer 1

Hint: We solve this problem by using the direct formula of simple interest that is
\[S.I=\dfrac{P\times T\times R}{100}\]
Here, \['P'\] is the principal amount
\['T'\] is the time period
\['R'\] is the rate of interest.
By using the above formula we calculate the simple interest and we add it to the principal value to get the total amount by the end of the period.

Complete step-by-step solution
We are given that the principal amount that Mrs. Gupta deposited in the bank as Rs. 10000
Let us assume that the principal value as
\[\Rightarrow P=10000\]
We are given that the interest rate is 1.5% per month
Let us assume that the interest rate as
\[\Rightarrow R=1.5\%\]
We are given that Mrs. Gupta deposited for a period of 5 years.
Let us assume that the period as
\[\Rightarrow T=5years\]
We know that if the interest is given per month then we need to convert the time period into months only.
We know that there are 12 months for 1 year.
By using this condition we get the time period of Mrs Gupta as
\[\begin{align}
  & \Rightarrow T=5\times 12 \\
 & \Rightarrow T=60months \\
\end{align}\]
We know that the direct formula of simple interest that is
\[S.I=\dfrac{P\times T\times R}{100}\]
Here, \['P'\] is the principle amount
\['T'\] is the time period
\['R'\] is the rate of interest.
By using the above formula we get the simple interest for Mrs. Gupta as
\[\begin{align}
  & \Rightarrow S.I=\dfrac{10000\times 1.5\times 60}{100} \\
 & \Rightarrow S.I=9000 \\
\end{align}\]
Now, let us assume that the total money that Mrs. Gupta gets at the end of 5 years as \['T'\]
We know that the total amount after the period that a person gets is calculated by adding simple interest to principal value.
By using the above result we get
\[\begin{align}
  & \Rightarrow T=10000+9000 \\
 & \Rightarrow T=19000 \\
\end{align}\]
Therefore, the total amount that Mrs Gupta gets after 5 years is Rs. 19000.

Note: Students may make mistakes in the time period.
We are given that the rate of interest at 1.5% per month then the time period should also be in the months not in the years.
So we have the time period as
\[\begin{align}
  & \Rightarrow T=5\times 12 \\
 & \Rightarrow T=60months \\
\end{align}\]
But, students may miss this point and take the time period in years only which gives the wrong answer.