Simple Interest and Compound interest shortcut formulas

Here you can find important formulas and time saving shortcut tricks and methods for simple interest and compound interest questions for various competitive exams

Simple Interest

Interest is said to be simple if it is calculated on the original principal throughout the loan period irrespective of the length of the period of which it is borrowed.

Simple interest is given by the formula I= PRT /100
Where P=PRINCIPAL R=RATE OF INTEREST per annum T=TIME PERIOD
Principal P=100I/RT
Rate of interest R=100I/PT
Time period T=100I/PR
If principal doubles in T years,then R=100/T
If principal triples in T years ,then R=200/T
if principal becomes four times in T years,then R=300/T

Compound Interest

When money is lent at compound interest the interest is calculated at fixed interval of time i.e,at the end of year, half year,quarterly, or even monthly etc.In such cases amount after first unit of time period becomes the principal for second unit of time period,the amount after second unit of time period becomes principal for third unit of time period and so on.

Compound interest is given by,

                                  
Where CI=Compound Interest,P=Principal,R=Rate of interest,T=Time period

 Amount after T years ,

                                      

• If rate is R1,R2 & R3 for 1st,2nd and 3rd year respectively then amount is ,

                              

• If difference of S.I and C.I is given for 2 years

                             

Example:Difference between simple interest on certain sum of money for 2 years at 4% and compound interest for same period at same rate is 200.Find the  sum

Ans:Principal=difference*(100/2)^2=200*100/2*100/2=RS 500000.

• If difference of S.I and C.I is given for 3 years                                  

• If amount compounded half yearly R will be replaced by R/2 and T will be replaced by 2T

                                     

• If amount compounded quarterly R will be replaced by R/4 and T will be replaced by 4T

                                            

• When the time is a fraction of a year say 2 1/5 years,

• If an amount A becomes B in T1 years ,then at T2 years 

Eg :Find the compound interest of Rs.10,000 in 9 months at 4%per annum interest payable quarterly.

Rate=4/4=1%,Time period= 9 months=3 quarter years.

CI=10,000*((1+1/100)^3 -1)=303.01.                                  

Alternative shortcut method for finding compound interest 

In some cases evaluation of C.I using formula will be time consuming. Here is an alternate method for calculating compound interest.

Let Principal= P, Compound interest % =  x % per annum , Time period=T

If T=2 , 

Total interest percentage for the first year=x,

Total interest percentage for the second year=x + x% of x= x+ (x*x/100)

Then effective percentage of interest =2x + x*x/100

Then C.I=(2 x + x*x/100) % of P= P*[(2x + x*x/100)/100]

If T=3

Total interest percentage for the first year=x,

Total interest percentage for the second year=x + x% of x= x+ (x*x/100)

Total interest percentage for the third year= x + x % of ( x + x+ x*x/100) =x+ x*( x + x+ x*x/100)/100)

Then effective percentage of interest= x+ x+ (x*x/100) + x+ x*( x + x+ x*x/100)/100)= 3x+ (x*x/100) +x*( 2x + x*x/100)/100)

You may be finding  formulas lengthy, but you will find this method simpler after practicing some problems.Especially if T=2, then this method will be much faster than conventional method using the commonly used formula.

Now let us solve two problems using above method.

Example 1 : What is the compound interest paid on a sum of Rs.3000 for the period of 2 years at 10% per annum.

1. 630
2. 620
3. 610
4. 600

Solution:    Interest % for 1st year= 10

                 Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11

                 Total % of interest= 10 + 11=21

                 Total interest = 21 % 3000= 3000 * (21/100)= 630

So, answer is option 1

Example 2:What is the compound interest paid on a sum of Rs.3000 for the period of 3 years at 10% per annum.

1. 900
2. 930
3. 990
4. 993

Solution= Interest % for 1st year= 10

                 Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11

                 Interest % for 3rd year= 10+ 10%(10+11)=10+ 2.1=12.1

                 Total % of interest= 10 + 11+12.1=33.1

                 Total interest = 33.1 % 3000= 3000 * (33.1/100)= 993

So, answer is option 4