Simple Interest math : simple interest formula, tricks and examples.

Simple Interest math:
Simple Interest
People need large amount of money for various reasons like buying a car, land, house, farm, education of children, etc..
Ordinary people always need money.
If this large amount is not readily available with us, we can borrow it from a bank or a co-operative credit society. This borrowed amount is called loan.
However, at the time of returning the loan to the bank or credit society, we have to pay back an amount somewhat bigger than the loan. This additional amount is called simple interest.
Suppose Sachin borrowed Rs 4,00,000 from a bank to buy a car. When he paid back his loan after two years, he gave the bank an amount of Rs 4,50,000. That is, he paid an additional amount of Rs 50,000. It means that he paid Rs 50,000 as simple interest.
The amount borrowed is called the principal. The principal period of time for which the amount is borrowed is called either ' period ' or ' time ' . In the above example, the principal is Rs 4,00,000 and the period or time is 2 years.
Rate of interest :
The interest to be paid for a loan depends upon the amount of the loan i.e. upon the principal. It also depends upon how long the loan was used i.e. upon the 'period' or ' time's.
To help calculate the interest, banks, credit societies, etc. That gives loans declared the amount that will have to paid as interest every year (per year) for Rs 100 of the principal borrowed (percent). This is call the rate of interest.
For example :
The rate of interest charged by Maharashtra Bank is 10 p.c.p.a. (per cent per annum / year) means that if a person takes a loan of Rs 100 for a year from this bank, then at the end of the year he must pay the bank an interest of Rs 10.
Interest depends on period :
The interest paid after two years on a certain principal will be twice that paid after one year on the same principal. In short, the interest will increase as many times as the period does.
For example :
1) What will be the interest after 4 years on Rs 100 at the rate of 12 p.c.p.a ?
Ans. :
Rate of interest is 12 p.c.p.a.
It means the interest on Rs 100 for 1 year is Rs 12.
Therefore, the interest on Rs 100 for 4 years will be 12 × 4 = Rs 48.
2) At a certain rate, the interest on a principal of Rs 20,000 at the end of one year is Rs 800. What will be the interest on the same principal after 5 years ?
Ans. :
The principal remains the same. The period has increased 5 times.
Therefore, internet will also increase five fold.
Therefore, after 5 years = 800 × 5 = Rs 4000.
Interest depends on principal :
If period remains the same the interest will increase as many times as the principal does.
Example :
1) If the rate is 12 p.c.p.a., what is the yearly interest on Rs 4000 ?
Ans :
Rate of interest : 12 p.c.p.a.
A year's interest on Rs 100 is Rs 12.
Principal is Rs 4000, i.e. 40 times 100.
Period, 1 year, same as before
Therefore, interest = 40 times Rs 12= 12 × 40 = Rs 480.
2) The interest for 3 years on Rs 8000 at a certain rate is Rs 600 . Then , What will be the interest for 3 years at the same rate on Rs 40,000?
Ans. :
Period is the same. Therefore the interest increases as many times as does the principal.
Rs 40,000 is 5 times Rs 8000.
Interest will be 5 times Rs 600.
Interest is 600 × 5 = Rs 3000.

The formula for Simple Interest :
Simple Interest = (principal × rate × period) / 100 
If we write I for Simple interest, P for principal, R for rate of interest and N for period ( Number of years ) .
I = ( P × R × N ) / 100
Example :
1) Find the interest on Rs 10,000 for 5 years at the rate of 11 p.c.p.a.
Ans. :
P = Principal = 10,000
R = Rate = 11
N = Number of year = 5
I = P × R × N  / 100
I = 10,000 × 11 × 5 / 100
I = 5500.
Therefore Simple Interest = 5500.
2) If Ram deposits Rs 4000 in the school fund at the rate of 10 p.c.p.a. for 5 years, what is the amount he will get at the end of the period?
Ans. :
Here, P = 4000, R = 10, N = 5
Therefore, I = P × R × N / 100
I = 4000 × 10 × 5 / 100
I = 2000.
Therefore, Ram will get the amount Rs 2000 at the end of the period.
When three of the four quantities principal, period, rate and amount are given, to find the fourth.
Example :
1) Principal = Rs 20,000 Rate = 10 p.c.p.a. Simple Interest = Rs. 5,000. Find the period.
Ans. :
Here, P = 20,000, R = 10, I = 5000, N = ?
I = P × R × N / 100
5000 = 20,000  × 10 × N / 100
5000 = 2000 × N
5 / 2 = N
Therefore, N = 2.5 year.

Amount :
Amount = Principal amount + Simple Interest
Example :
Sham borrowed Rs 10,000 from a bank at 10 p.c.p.a and after 2 years returned Rs 12,000 at the bank to pay back the debt in full. What is the extra amount he paid back?
Here the principal is Rs 10,000 the time is 2 years and rate of interest is 10 P.c. P.a.
He paid back Rs 12,000. It means he paid 12,000 - 10,000 = Rs. 2000 extra.
Thus the simple interest is Rs 2000.
Amount = Principal amount + Simple Interest
Here, the amount is Rs. 12000.
Therefore,
Amount = Principal amount + Simple Interest
Simple Interest = Amount - Principal

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