# CLASS-5SIMPLE INTEREST BY UNITARY METHOD

SIMPLE INTEREST BY UNITARY METHOD -

To calculate simple interest using the unitary method, you need to follow these steps:

1. Determine the principal amount (P), interest rate (R), and time period (T).
2. Convert the interest rate (R) into a decimal. For example, if the interest rate is 5%, you would convert it to 0.05.
3. Calculate the interest for one unit of time by multiplying the principal (P) by the interest rate (R).Interest for one unit of time = P * R
4. Multiply the interest for one unit of time by the actual time period (T) to find the total interest.Total interest = (P * R) * T

Remember :-

1Principal is denoted by the letter P.

2Rate of Interest is denoted by the letter R.

3Time is denoted by the letter T.

4Simple Interest is denoted by S.I.

5 Amount is denoted by the letter A.

Formulae for Calculating Simple Interest :-

Ø  Amount = Principal + Simple Interest

Ø  Principal = Amount – Simple Interest

Ø  Simple Interest = Amount – Principal

Principal × Rate × Time

Ø  Simple Interest = -------------------------

100

𝐏 × 𝐑 × 𝐓

or, S.I. = -----------

𝟏𝟎𝟎

Let's consider an example :-

Suppose you have a principal amount of \$1,000, an interest rate of 8%, and a time period of 3 years.

Step 1: P = \$1,000, R = 8% (convert to 0.08), T = 3 years

Step 2: R = 0.08

Step 3: Interest for one unit of time = \$1,000 * 0.08 = \$80

Step 4: Total interest = \$80 * 3 = \$240

Therefore, the total interest earned in this example is \$240.

In the context of simple interest, the unitary method is a technique that can be used to find various components of the formula (principal, interest, or time) when the other components are known. The unitary method is based on the concept of finding the value of one unit and then using that value to calculate the desired quantity.

Let's break down the unitary method for simple interest :-

1. Finding the interest: To calculate the interest, we need to know the principal (P), interest rate (R), and time (T). If the principal, rate, and time are given, you can find the interest using the following steps:
• Determine the value of one unit of time (1 year, for example). Let's call it V.
• Calculate the interest for the given time using the formula: I = (P * R * V).
1. Finding the principal: To determine the principal, we need to know the interest (I), interest rate (R), and time (T). If the interest, rate, and time are given, you can find the principal using the following steps:
• Determine the value of one unit of time (1 year, for example). Let's call it V.
• Calculate the principal using the formula: P = (I / (R * V)).
1. Finding the time: To calculate the time, we need to know the principal (P), interest (I), and interest rate (R). If the principal, interest, and rate are given, you can find the time using the following steps:
• Determine the value of one unit of interest (1 unit of interest corresponds to 100 units of principal). Let's call it V.
• Calculate the time using the formula: T = (I / (P * R * V)).

By applying the unitary method, you can find the missing component (principal, interest, or time) in the simple interest formula based on the given values. Remember to be consistent with the units used (e.g., if the interest rate is given annually, the time should be in years).

1) Find the S.I. by unitary method :-

a) \$ 1200 for 3 years at 5 % per annum

Ans.) Interest on \$ 100 for 1 year = \$ 5

5

Interest on \$ 1 for 1 year = \$ -------

100

5

.: Interest on \$ 1200 for 1 year = \$ ------- × 1200

100

5

.: Interest on \$ 1200 for 3 years = \$ ------- × 1200 × 3

100

[100 and 1200 have the common factor 100]

5

= \$ ------- × 12 × 3

1

5 × 12 × 3

= \$ --------------

1 × 1 × 1

= \$ 180          (Ans.)

b) \$ 900 for 2 year 4 months at 4 % per annum

Ans.)

4

2 years 4 months = 2 ------- years   [Since, 1 year = 12 months.

12

[4 and 12 have the common factor 2 & 2 and 6 have the common factor 2]

1

= 2 ------- years  [Convert the mixed number into improper fraction]

3

(2 × 3) + 1                7

= ------------- years = ------- years

3                       3

Interest on \$ 100 for 1 year = \$ 4,

4

Interest on \$ 1 for 1 year = -------

100

4

So, Interest on \$ 900 for 1 year = \$ ------- × 900

100

7                 4 X 900         7

Now, Interest on \$ 900 for ------- years = ---------- X -------

3                   100            3

[100 and 900 have the common factor 100 & 9 and 3 have the common factor 3]

4 × 3 × 7

= \$ ------------- = \$ 84       (Ans.)

1 × 1 × 1

1

c)  \$ 250 for 3 ------ years at 9 % per annum

2

Ans.)

1                 (3 × 2) + 1                7

3 ------- years = ------------- years = ------- years

2                      2                      2

[Convert the mixed number into improper fraction]

Interest on \$ 100 for 1 year = \$ 9

9

Interest on \$ 1 for 1 year = \$ -------

100

9

So, Interest on \$ 250 for 1 year = \$ ------ × 250

100

7                   9 X 250         7

So, Interest on \$ 250 for ------ years = \$ ----------- X ------

2                     100            2

[100 and 250 have the common factor 100 & 10 and 25 have the common factor 5]

9 × 5 × 7           315

= \$ ------------ = \$ -------

2 × 1 × 2            4

= \$  78.75       (Ans.)