Tricks on Simple Interest
Simple Interest (SI)
If the interest on a sum borrowed for a certain period is calculated uniformly, it is called simple interest(SI). (fix percentage of principal)
What is Principal (sum)?
Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P.
What is Amount?
The Addition of Simple Interest and Principle is called the Amount.
A = S.I + P (Principal)
Interest is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed calculated on the basis of Principle.
This is the duration for which money is lent/borrowed.
Rate of Interest
It is the rate at which the interest is charged on principal.
What does per annum mean?
"Rate of interest R% per annum" means that the interest for one year on a sum. If not stated explicitly, the rate of interest is assumed to be for one year.
Formulas Need to Remember:
S.I =[( P X R X T )/( 100 )].
Where P = Principle, R = Rate of per annul, T = Number of years
From the above formula, we can derive the followings
Some Tricks to Solve easily
Trick 1:- If a sum of money becomes “n” times in “T years” at simple interest, then the rate of interest per annum can be given be
Trick 2:- If an amount P1 is lent out at simple interest of R1% per annum and another amount P2 at simple interest rate of R2% per annum, then the rate of interest for the whole sum can be given by
Trick 3:- A sum of money at simple interest n1 itself in t1 year. It will become n2 times of itself in (If Rate is constant)
Trick 4:- In what time will the simple interest be “n” of the principal at “r %” per annum:-
rt =n x 100
Trick 5:- If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R1, R2, ... , Rn respectively and time periods are T1, T2, ... , Tn respectively, then the ratio in which the sum will be divided into n parts can be given by
Some Important examples based on Simple Interest
Example 1: A sum amounts to Rs. 702 in 2 years and Rs. 783 in 3 years. Calculate the sum, rate of interest and the amount after 5 years?
Amount for 2 years(A2) = 702
Amount for 3 years (A3)= 783
Interest for 1 year (I) = 783-702 = 81
So Sum = A2 – 2I = 702 – 2×81
= 702-162 = 540
rate of interest = (81/540)×100
Amount after 5 years = Sum+5I
= 540+ 5×81
Example 2: A sum of money doubles itself in 3 yrs at simple interest. In how many yrs will it amount to 8 times itself?
Solution: Doubles in 3 yrs
3 times in 3× 2 = 6yrs
4 times in 3× 3 = 9yrs
8 times in 3× 7 = 21yrs
Example 3: Atul and Vijay are friends. Atul borrowed a sum of Rs.400 at 5% per annum simple interest from Vijay. He returns the amount with interest after 2 yrs. Vijay returns to Atul 2% of the total amount returned. How much did Atul receive?
Solution: After 2 yrs, amount returned to Vijay = 400+ (400*5*2)/100 = Rs 440
Amount returned to Atul = 2% of 440 = 8.8
Annual Instalments for Simple Interest:
Let's discuss a real example to understand instalment concepts:
A person deposit Rs.140 to the bank every year up to 5 yrs. The bank gives him a 5% rate of interest simple annually. And at the end of 5 yrs, he gets total amount of Rs.770
So, 140 is the instalment, time is 5 years rate of interest is 5% and the amount or debt is Rs.770
This Instalment is also known as an annual payment. Debt is the total amount, so don’t confuse between these two terms.
Installment = where A = debt, r = rate of interest and t = time period
Example 4: What annual payment will discharge a debt of Rs.848 in 4yrs at 4% per annum simple interest?
In case if you forget formula then how to approach this question.
Let installment is X. There are 4 installments and rate of interest is also 4%
Debt (A) = four installments + (r%) × installments × (0+1+2+… (t-1))
So, 848 = 4X + (4%)(X)(0+1+2+3)
848 = 4X+
848 = 4X+
848 = 424X/100
X = 200
Example 5: Rs.4000 is divided into two parts such that if one part be invested at 3% and the other at 5%, the annual interest from both the investments is Rs. 144. Find each part.
Solution: Let the amount lent at 3% rate be Rs.X, then amount lent at 5% rate is 4000-X
So, 3% of X + 5% of (4000-X) = 144
5% of 4000 – 2% of X = 144
200 – 2% of X = 144
2% of X = 56
X = (56/2)×100
X = 2800
4000 - X = 1200
How to solve this Question by Alligation Method:
First we will calculate net rate of interest for Rs. 144 on 4000
So, net rate = (144/4000)× 100 = 3.6%