# SIMPLE INTEREST (SI) AND COMPOUND INTEREST (CI) math capsule

Tags: money rate amount
How much is my bank going to pay me for depositing a certain amount of money into my bank account?
Has this question came into your mind ? If yes, then you are going to master all ways how you can calculate this in this blog post on SI and CI.

## SIMPLE INTEREST :

When we borrow some Money , then customarily the money lender or the person who is giving us the money uses to charge some extra amount of money in lieu of the money that he has lent us.This extra money by the money lender is called Interest.

Principal
This is the amount of money that is borrowed from a money lender that is the starting or initial amount you ask the money lender for.It is denoted by 'P'.

Amount
This is the sum that is the addition of two things , one the principal and , other the interest . It is denoted by 'A'.

A= Principal + Interest , here the interest is simple interest

Rate
This is the interest paid on a reference on rs 100 for a specified period of time .It is denoted by 'R'.

Time
The time period for which the money is lent or deposited or borrowed is called time and it is denoted by 'T'.

Simple Interest
simple interest refers to the interest which is calculated on the original amount (principal) for any given time and Rate of interest .It is denoted by 'SI'.

### SIMPLE INTEREST =(P*R*T)/100

,where , P = principal , R=rate of interest and , T= time period

Q. calculate the simple interest on rs 5000 for 3 years having a rate of interest as 5%.
A.
SI= P*R*T/100
= (5000*3*5)/100 = 750
Q. find out the simple interest on rs 6000 for 5 years with a rate of interest 7%.
A.
SI=P*R*T/100
=(6000*5*7)/100 =2100

Simple Interest for every year remains the same whereas , compound interest changes from year to year.

### SOME OTHER RULES RELATED TO SIMPLE INTEREST -

• If the amount of money becomes n times in 'T' years at simple interest , then rate of interest will be,                                                                          R=[100*(n-1)/T]%
• If a certain principal amounts to rs A1 in t1 years ,and rs A2 in t2 years , then the sum is given by,                                                                                [(A2*t1-A1*t2)/(t1-t2)]
• If a sum of money becomes n1 time of itself in t1 years at the rate of simple interest , then time taken to be n2 times will be,                                       t2=(n2-1)*t1/(n1-1)
• The annual payment that will discharge a debt of rs A due in t years at the rate of interest r% per annum is ,                                                              [(100*A)/(100*t+r*t*(t-1)/2)]
Nice ?
Thanks , here are some exercises for you :)

 SI EXERCISE 1
 SI EXERCISE 2

 HINTS AND SOLUTIONS 1

 HINTS AND SOLUTIONS 2

 HINTS AND SOLUTIONS 3

## COMPOUND INTEREST:

If the principal does not remain the same for the entire loan period, due to addition of interest accrued to the principal after a certain interest of time to form the new principal.This process is repeated until the amount for the given time is found. The difference between the final amount and the original principal is called compound interest and it is denoted by 'CI'.
If the interest is compounded annually, then the principal changes after every year and if the interest is compound half yearly or quarterly , then the principal changes after every 6 months or 3 months.

### FORMULAES FOR COMPOUND INTEREST:

• When interest is compounded annually, Then rate of interest = R% per annum and n= number of years,    (1) amount = P*(1+R/100)^n         (2) CI = A-P = P[(1+R/100)^n  -1]
• When interest is compounded half yearly (6 months), then rate of interest will be half and time will be , i.e.,  n=T*2  , rate =R/2
• When interest is compounded quarterly (3 months ), then rate of interest will be one fourth and time will be four times.
• When interest is compounded annually but time is given in fraction (let time , t=a/b years), then,       amount =P(1+R/100)^t   *  (1+(a/b)R)/100
• When rate of interest for n1,n2 and n3 years are R1, R2 and R3 respectively, then                              amount =P(1+R1/100)^n1 * (1+R1/100)^n2 *(1+R2/100)^n3

### EXERCISES FOR COMPOUND INTEREST :

 CI EXERCISE 1

 CI EXERCISE 2

 HINTS AND SOLUTIONS 1

 HINTS AND SOLUTIONS 2

 HINTS AND SOLUTIONS 3

 HINTS AND SOLUTIONS 4
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