Question

On what sum of money lent out at 9% per annum for 6 years does the simple interest amount to Rs. 810?
A) Rs. 1000
B) Rs. 1500
C) Rs. 1200
D) None

Answer 1

Hint: We have been given the rate of interest, time and simple interest for a certain amount of money lent. This money can be calculated by substituting the known values in the formula for Simple Interest which is:
  $ S.I = \dfrac{{P \times R \times T}}{{100}} $ where, S.I is the Simple Interest. P is the principal, R is the rate and T is the duration of time for which the money is lent.

Complete step-by-step answer:
We have been given:
The sum of money is lent out at the rate 9% per annum
R = 9%
Duration of this lent money is 6 years
T = 6
The simple interest on the money is Rs. 810
S.I = Rs. 810
Let the sum of money which is the principal amount b x.
 P = x
The formula for Simple Interest (SI) is given as:
  $ S.I = \dfrac{{P \times R \times T}}{{100}} $
Substituting the values, we get:
  $ 810 = \dfrac{{x \times 9 \times 6}}{{100}} $
Calculating the value of x:
  $
   \Rightarrow x \times 9 \times 6 = 810 \times 100 \\
   \Rightarrow x = \dfrac{{810 \times 100}}{{9 \times 6}} \\
   \Rightarrow x = Rs.1500 \;
   $
The principal amount lent is Rs. 1500
Therefore, the required sum of money that is lent out at 9% per annum for 6 years for which the simple interest amounts to Rs. 810 is Rs. 1500
So, the correct answer is “Rs. 1500”.

Note: When the money is borrowed, the lender lent that money at an extra charge on the borrowed money. This charge is known as interest which can be simple and compound and the money borrowed is known as principal amount. S.I and P are related to monetary and thus are known as amount but the ‘amount’ in case of interest is the sum of interest and principal money. The given amount in question is that of the SI and should not be confused with the other amount that is finally received after the total accumulation of interest over the time.