Question

A girl deposits 300rs in a bank account. The bank offers 7% interest per year. Assuming the girl does not take any money out of the account. Calculate the total amount of money after 1 year.

Answer 1

Hint: According to the question given above we have to calculate the amount of money when the bank provides the 7% of interest per year. As given in the question a girl deposits 300rs per month in her bank account hence, first of all we have to calculate the principal amount which can be calculated by multiplying the deposit amount to the time of deposition which is 12 months/1year for the given question. Now, as given in the question bank offers 7% interest per year so, we have to find the interest rate per month (R) which can be calculated by dividing the rate of interest per year by time which is 12 months.
Now, to find the interest of money after 12 months (1-year) on the amount deposited by the girl we will use the formula to calculate the simple interest for the given months/years as given below.
Simple interest = $\dfrac{{P \times R \times T}}{{100}}$
Where, P is the principal amount, R is the rate of interest and T is the time period.
Now, after finding the simple interest we have to calculate the total amount (which is the sum of principal amount and the simple interest)

Complete step-by-step answer:
Given,
Deposit amount by the girl per month (P) = 300rs,
Interest rate offer by the bank per year (R) = 7%
Step 1: To calculate the simple interest first of all we have to find the principal amount which can be calculated by multiplying the deposit amount to the time of deposition which is 12 months/1year for the given question.
Principal amount = amount deposit/month $ \times $the duration of amount deposit in the bank account…………………….(2)
Step 2: On substituting all the values above in (2),
Principal amount: $300 \times 12 = 3600rs$
Step 3: Now, to find the interest rate per month which can be calculated by dividing the rate of interest per year which is 7% as given in the question by time which is 12 months.
Interest rate per month (R)$ = \dfrac{7}{{12}}$
Step 4: Now, we have to calculate the simple interest when the bank provides the 7% of interest per year on the amount deposited by the girl for 12 months/1 year. On substituting all the values in formula (1)
Simple interest $ = \dfrac{{3600 \times \dfrac{7}{{12}} \times 12}}{{100}}$
On solving the expression obtained above,
Simple interest$ = 36 \times 7$
Simple interest$ = 252rs$
Step 5: Now, we can calculate the total amount which can be obtained by the sum of principal amount and the simple interest.
$
   = 3600 + 252 \\
   = 3852rs \\
 $
Hence, total mount $ = 3852rs$

The total amount of money after 1 year at 7% interest per year provided by the bank is $ = 3852rs$

Note: As, the bank offers 7% interest per year so we have to calculate the interest rate per month (R) which can be calculated by dividing the rate of interest per year by time which is 12 months.
To find the simple interest it is necessary to calculate the principal amount for the given time.
If, the time of interest or deposition is given in month then we convert it in months to calculate the simple interest.
If, the interest on a sum of money is $\dfrac{1}{x}$ of the principal amount, and the number of years is equal to the rate of interest then rate can be calculated by using the formula: $\sqrt {\dfrac{{100}}{x}} $