CLASS-6
FINDING SIMPLE INTEREST THROUGH ALGEBRAIC METHOD

FINDING SIMPLE INTEREST THROUGH ALGEBRAIC METHOD -

Solving problems involving simple interest using algebraic methods is straightforward. The formula for simple interest is:-

                                                    I = P X R X T

Where:-

• I is the interest earned or paid,
• P is the principal amount (the initial sum of money),
• R is the interest rate (expressed as a decimal), and
• T is the time (in years) the money is invested or borrowed for.

To solve simple interest problems algebraically, you need to rearrange this formula based on what you're trying to find. There are three main scenarios you might encounter:

1) Finding the Interest (I):- If you know the principal (P), interest rate (R), and time (T), you can solve for the interest (I) using the formula as is.  I = P X R X T

2) Finding the Principal (P):- If you know the interest (I), interest rate (R), and time (T),

                                                                                                                       I

you can rearrange the formula to solve for the principal (P): P =  --------------- 

                                                                                                                   R X T

3) Finding the Rate (R):- If you know the principal (P), interest (I), and time (T), you can

                                                                                                               I

rearrange the formula to solve for the interest rate (R): R = ----------------

                                                                                                           P X T

4) Finding the Time (T):- If you know the principal (P), interest (I), and interest rate (R),

                                                                                                             I

you can rearrange the formula to solve for the time (t): T = --------------

                                                                                                         P X R

Let's go through an example of each scenario/Example:-

Example.1)  Finding the Interest (I): Suppose you have a principal of $5,000, an interest rate of 0.05 (5%), and the money is invested for 3 years. Find the interest earned.

Ans.) As per the given condition, the formulae to be applied -

          I = P X R X T = 5000 X 0.05 X 3

 =>    I = 5000 X 0.05 X 3 = 750 = 750

So, the interest earned is $750.         (Ans.)

Example.2) Finding the Principal (P): Suppose you have earned $400 in interest at an interest rate of 0.06 (6%) over 2 years. Find the principal.

Ans.) As per the given condition, the formulae to be applied -

                       I

     P =  ----------------- 

                  R X T

                   4000

     P = ------------------

                0.06 X 2

                   4000

     P = ------------------

                    0.12

     P = 3333.33

The principal amount is approximately $3,333.33.    (Ans.)

Example.3) Finding the Rate (R): Suppose you have $2,500 invested for 4 years and earned $600 in interest. Find the interest rate.

Ans.)  As per the given condition, the formulae to be applied -

                         I  

          R = ---------------

                      P X T

                       600

         R = -----------------

                   2500 X 4

              =   0.06 = 6%

So, the interest rate is 6%.     (Ans.)

Example.4) Finding the Time (t): Suppose you have $8,000 invested at an interest rate of 0.04 (4%), and you earned $960 in interest. Find the time.

Ans.)  As per the given condition, the formulae to be applied -

                         I

        T = ------------------ 

                     P X R

                          960

        T = ----------------------

                   8000 X 0.04

                       12

        T = ------------------

                 100 X 0.04

         T =  3

The money was invested for 3 years.         (Ans.)