SIMPLE INTEREST
As we know that, the additional amount a borrower pays for the use of the sum anybody borrows is called the interest (I). There are some simple information is to be remembered –
1) The time (T) is the fixed period for which the money is taken as a loan.
2) The principle (P) is the sum of money lent or borrowed.
3) The amount (A) is the sum of the principal and the interest
A = P + I,
P = A – I,
And, I = A – P
4) The rate (R) is the interest paid on $ 100 per unit of time, it is usually understood to be per annum or per year.
5) Simple interest is the interest on a fixed principle for a given period of time at the same rate of interest. It is calculated by the following formula.
P X R X T
I = -----------------------
100
Principal (P) X Rate (R) X Time (T)
Interest (I) = -----------------------------------
100
Here, ‘R’ is the rate of interest per annum and ‘T’ is in years.
I X 100 I X 100 I X 100
Thus, T = -----------, R = ------------, P = ------------
P X R P X T R X T
Some Important Notes –
In calculating the interest for a period between two given dates, assume that a year contains 365 days even if it is a leap year.
In calculating the time, count either the day of borrowing or the day of repayment. For example, if the date of borrowing is 8th June 2019 and the date of repayment is 30th June 2019, then the interest will be calculated from 9th June 2019 to 30th June 2019 or from 8th June 2019 to 29th June 2019.
The unit of time should be the same for ‘T’ and ‘R’. Thus if ‘R’ is per annum then change ‘T’ to years and if ‘R’ is per month and ‘T’ is in years, change ‘T’ to months or ‘R’ to per annum.
1 year = 12 months = 365 days
In calculating the period between two dates, only one of the days is counted.
Find out the principal in each of the following cases -
a) Interest = $ 10, rate = 5 % per annum, time = 5 years
I X 100 10 X 100
Ans.) P = ----------- = ------------ = $ 40 (Ans.)
R X T 5 X 5
b) Interest = $ 50, rate = 10 % per annum, time = 5 years 5 months
I X 100 50 X 100
Ans.) P = ----------- = ------------- = $ 92.3 (Ans.)
R X T 10 X 65/12
c) Interest = $ 98 , rate = 10 % per annum, time = 8 years 2 months
I X 100 98 X 100
Ans.) P = ------------ = ------------- = $ 120 (Ans.)
R X T 10 X 49/6
Find out the rate of simple interest per annum in each of the following cases -
a) Principal = $ 2500, interest = $ 500, time = 5 years 6 months
I X 100 500 X 100
Ans.) R = ------------ = -------------- = 3.64 % (Ans.)
P X T 2500 X 11/2
b) Principal = $ 4500, interest = $ 500, time = 2 years 6 months
I X 100 500 X 100
Ans.) R = ------------ = -------------- = 4.44 % (Ans.)
P X T 4500 X 5/2
c) Principal = $ 3300, interest = $ 800, time = 3 years 4 months
I X 100 800 X 100
Ans.) R = ------------ = -------------- = 7.30 % (Ans.)
P X T 3300 X 10/3
Find out the time in each of the following cases –
1
a) Principal = $ 50000, interest rate = 2 ------- % per annum ,
2
Interest = $ 15000
I X 100 15000 X 100
Ans.) T = ----------- = --------------- = 12 years (Ans.)
P X R 50000 X 5/2
1
b) Principal = $ 35000, interest rate = 3 ------- % per annum ,
2
Interest = $ 5000
I X 100 5000 X 100
Ans.) T = ----------- = --------------- = 4.08 years (Ans.)
P X R 35000 X 7/2
1
c) Principal = $ 5500, interest rate = 5 ------- % per annum,
2
Interest = $ 1100.
I X 100 1100 X 100
Ans.) T = ----------- = --------------- = 3.63 years (Ans.)
P X R 5500 X 11/2