# CLASS-5SIMPLE INTEREST BY FORMULAE METHOD

SIMPLE INTEREST BY FORMULAE METHOD -

To calculate simple interest using the formula method, you can use the following formula:

Simple Interest (SI) = (Principal × Rate × Time) / 100

Where :-

• Principal refers to the initial amount of money borrowed or invested.
• Rate represents the interest rate per time period.
• Time denotes the duration for which the money is borrowed or invested.

To calculate the simple interest, follow these steps :-

1. Identify the values of Principal, Rate, and Time.
2. Substitute the values into the formula.
3. Multiply Principal, Rate, and Time.
4. Divide the product obtained in step 3 by 100.
5. The result will be the simple interest.

Here's an example to illustrate the calculation :-

Suppose you borrow \$5,000 at an interest rate of 8% per year for a period of 3 years.

Principal (P) = \$5,000,

Rate (R) = 8%,

Time (T) = 3 years,

Using the formula, we can calculate the simple interest (SI) :-

SI = (P × R × T) / 100 = (5000 × 8 × 3) / 100 = 1200

Therefore, the simple interest on the loan would be \$1,200.

The formula for calculating simple interest is:

I = P ⋅ R ⋅ T

Where :-

• I represents the interest amount
• P is the principal amount (the initial amount of money)
• R is the rate of interest (expressed as a decimal)
• T is the time period (in years)

To find the simple interest using this formula, follow these steps:

1. Determine the principal amount (P), which is the initial sum of money.
2. Identify the rate of interest (R). This can be given as a percentage, so make sure to convert it to a decimal by dividing by 100. For example, if the interest rate is 5%, R would be 0.05.
3. Determine the time period (T), usually in years.

Once you have these values, you can plug them into the formula to calculate the simple interest (I).

For example, let's say you have a principal amount of \$1,000, an interest rate of 5% (0.05 as a decimal), and a time period of 3 years. Using the formula, the calculation would be:

= 1000⋅0 X 05⋅3 = 150 I = 1000⋅0 X 05⋅3 = 150

Therefore, the simple interest on a \$1,000 principal amount at an interest rate of 5% over a period of 3 years would be \$150.

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

a) \$ 600 for 1 year at 4 % per annum

Ans.)

P = \$ 600,

R = 4 %,

T = 1 year

P × R × T            600 × 4 × 1

S.I. = ------------- = \$ ---------------

100                    100

[600 and 100 have the common factor 100]

6 × 4 × 1

= \$ ------------ =  \$ 24      (Ans.)

1 × 1

1

b) Rs. 1800 for 2 years at 4 ------ % per annum

2

Ans.)

1

R = 4 ------ %    [Convert the mixed number into improper fraction]

2

(4 X 2) + 1               9

= -------------- %  =  ------ %

2                     2

P = \$ 1800, T = 2 years

1800 × 9 × 2

S.I. = \$ ---------------

100 × 2

18 × 9 × 2

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

1 × 2 × 1

[1800 and 100 have the common factor 100 & equal factors in numerator and denominator is 2]

18 × 9 × 1

= \$ -------------- = \$ 162            (Ans.)

1 × 1 × 1

c)  Rs. 9000 for 146 days at 5 % per annum (1 year = 365 days)

Ans.)

146

T = 146 days = -------- year    [Since, 1 year = 365 days]

365

P = \$ 9000, R = 5 %

9000 × 5 × 146

S.I. = \$ ------------------

100 × 365

[365 and 5 have the common factor 5, 146 and 73 have the common factor 73 & 9000 and 100 have the common factor 100]

2 × 90 × 1

=  \$ -------------- = \$ 180          (Ans.)

1 × 1 × 1

d)  Rs. 18,000 for 6 months at 10 % per annum

6

T = 6 months = ------ year    [Since, 1 year = 12 months.]

12

[6 and 12 have the common factor 6]

P = \$ 18,000, R = 10 %

18000 × 10 × 1

S.I. = \$ -----------------

100 × 2

180 × 5 × 1

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

1 × 1 × 1

[18000 and 100 have the common factor 100 & 10 and 2 have the common factor 2]

=  \$ 900            (Ans.)