SIMPLE INTEREST BY UNITARY METHOD -
To calculate simple interest using the unitary method, you need to follow these steps:
Remember :-
1) Principal is denoted by the letter P.
2) Rate of Interest is denoted by the letter R.
3) Time is denoted by the letter T.
4) Simple 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 :-
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.)