Question

Find the principal when the following are given.
 \[I = Rs.192{\rm{ Rate = 6\% }}\] Per annum \[Time = 4{\rm{ years}}{\rm{.}}\]

Answer 1

Hint: First look at definitions of interest, principal, rate, time in the concept of simple interest. Now use the relation between these 4 variables. Find the \[{4^{th}}\] one. Now try to keep all the 3 known variables on the right hand side then try to bring the unknown variable on the left hand side. So the simplified value of the right hand side of the equation will be equal to the value of the unknown variable. This unknown variable’s value is the required result in the question.

Complete step-by-step answer:
Principal: - In terms of simple interest, we say that the original sum which is taken or deposited at start of the process is defined as principal amount. It is denoted by variable P.
Interest: - In terms of simple interest, we say that the amount of money which we pay to borrow money or amount of money which you earn on a deposit of money is called interest. It is denoted by I.
Rate: - In terms of simple interest we say that the interest rate is the amount a lender charges for the use of assets expressed as a percentage of principal. This rate is typically on an annual basis, also known as the annual percentage rate. It is denoted by R.
Time: - In terms of simple interest, we say that the duration for which the money is borrowed or the duration for which the money is deposited is called time. It is denoted by T.
By basic knowledge of simple interest, we know the relation
 \[I = \dfrac{{PRT}}{{100}}\] . . . . . . . . . . . . . . . . . (1)
This formula can be verified by above definitions.
Rate is percentage of \[P = \dfrac{{PR}}{{100}}\]
T is the duration we used. So, \[I = \left( {\dfrac{{PR}}{{100}}} \right)T\]
Given the value of interest in the question to be as:
Rs.192
By this we get the value of variable I to be as:
 \[I = 192\] . . . . . . . . . . . . . . . . (2)
Given the value of rate in the question to be as:
6% per annum
By this we get the value of variable R to be as:
 \[R = 6\] . . . . . . . . . . . . . . . . . . (3)
Given the value of time in the question to be as:
4 years
By this we get the value of variable T to be as:
 \[T = 4\] . . . . . . . . . . . . . . . . . . . (4)
By substituting the values I, R, T from equation (2), (3), (4), we get:
 \[192 = \dfrac{{P \times 6 \times 4}}{{100}}\]
By simplifying numerator and cross multiplying, we get it as:
 \[19200 = P \times 24\]
By dividing with 24 on both sides, we get it as:
 \[P = \dfrac{{19200}}{{24}}\]
By simplifying above equation, we get value of P as:
 \[P = 800\]
The value of principal amount in question is Rs.800

Note: Be careful with definition, formula. Percentage symbol is already included in the formula by 100. Students forget this and again keep a 100 to satisfy percentage sign but it is wrong. In that way you will get wrong results. Be careful while substituting the values. Students generally confuse and substitute P in place of I.