Question

Mahesh deposited Rs 8650 in a bank at the rate of \[6\] p.c.p.a. How much money will he get at the end of the year in all?

Answer 1

Hint: We will use the concept of simple interest to solve the given problem. We will use the value of the principal, the rate of interest and the time period to calculate the simple interest. We will then add obtained simple interest to the principal to calculate the amount received by Mahesh at the end of the year.

Formula used:
We will use the following formulas:
1.Simple Interest, \[S.I = \dfrac{{P \times r \times t}}{{100}}\], where \[P\] is the principal amount, \[r\] is the rate of interest and \[t\] is the time period (in years).
2.Amount, \[A = P + S.I\]

Complete step-by-step answer:
It is given to us that Mahesh has deposited Rs 8650 in a bank at the rate of \[6\% \] per annum.
We have to find the total amount he will receive at the end of the year i.e., one year from making the deposit.
Substituting, \[P = 8650\], \[r = 6\% \] and \[t = 1\] in the formula of simple interest, \[S.I = \dfrac{{P \times r \times t}}{{100}}\], we get
\[S.I = \dfrac{{8650 \times 6 \times 1}}{{100}}\]
Multiplying the terms in the numerator, we get
\[ \Rightarrow S.I = \dfrac{{51900}}{{100}}\]
Dividing 51900 by 100, we get
\[ \Rightarrow S.I = 519\]
Therefore, the amount of interest received by Mahesh is Rs 519.
Now, we have to calculate the total amount Mahesh receives at the end of the year including the interest.
Substituting the principal amount \[P = 8650\] and the simple interest \[S.I = 519\] in the formula \[A = P + S.I\], we get
\[A = 8650 + 519\]
Adding the terms, we get
\[ \Rightarrow A = 9169\]
Therefore, the amount Mahesh receives at the end of the year is Rs 9169.

Note: Simple interest calculates the total interest payment using a fixed principal amount. The interest that is collected over time is not added to the principal amount. On the other hand, Compound interest calculates the total interest payment using a variable principal amount. The interest that is collected over time is added to the principal amount.