Published by: Divyanshu Nayak 
What is Simple Interest?
Simple interest is the form of calculating interest where interest is calculated only on the principal and calculated uniformly through all the intervals then the interest is called simple interest. in this case the Principal remains Constant throughout the duration.
Some Important Terms:-
Principal: An amount of money that you lend to somebody or invest to earn interest. It is usually denoted by the letter ‘ p ‘
Interest: The extra money that you receive when you invest money or payback when you borrow money. It is usually denoted by SI or CI depending upon the calculation. it is the difference of the Amount and Principal ( A – P )
Time / Period: Time or period for which is borrowed or invested it is usually denoted by ‘t‘
Rate of interest: Rate at which interest is calculated on the principal. It is a percentage value calculated as % per/ annum, denoted by ‘r‘
Amount: Principal + Interest (for a given period at a given rate of interest) this is usually denoted by ‘ A ‘
Tips and Tricks for solving Simple Interest and Compound Interest Related questions.
Quick List of Formulae ( Simple Interest )
- SI = ( P x R x T ) / 100
- P = Principal
- R = Rate of Interest % p.a
- T = Time Interval
- P = ( 100 x SI ) / ( R x T )
- R = ( 100 x SI ) / ( P x T )
- T = ( 100 x SI ) / ( P x R )
- Amount = P + SI = A
- Interest Acquired = A – P = (PRT) / 100
- If a sum becomes N times in t years, then RT = 100 ( N – 1 )
- OR R = ( N – 1 ) / T × 100 %
If R = T then,
Example:- 1 Find simple interest on ₹ 2000 at 5% per annum for 3 years. Also, Find the amount.
Solution:
Principal = ₹ 2000
Rate = 5% p.a.
T = 3 years
S.I = (P × R × T) / 100
= (2000 × 5 × 3)/100
S.I = ₹ 300
Amount = P + S.I
= ₹ ( 2000 + 300 ) = ₹ 2300
Example 2. A sum amounted to ₹ 2520 at 10% p.a. for the period of 4 years. Find the sum
Solution:
Let A = ₹ 2520
R = 10% p.a.
T = 4 years
P = x
Let the Principal be x
S.I = (P × R × T) / 100
S.I = ( x × 10 × 4) / 100 = 40x / 100 = 2x / 5
A = P + I
A = x + 2x/5
A = (5x + 2x)/5 = 7x/5 [But given that A = ₹ 2520]
7x/5 = 2520
7x = 2520 × 5
x = (2520 × 5) / 7 = ₹ 1800
Example 3. At what rate per cent per annum simple interest will a sum of money double itself in 6 years?
Solution:
Let P = x, then A = 2x
Also, S.I = A – P
= 2x – x
= x
Therefore:- S.I = P
T = 6 years
We know that S.I. = (P × R × T) / 100
(x × R × 6)/100 = x
R = 100x/6x = 16.6 %
Example 4. In how much time will a sum of money triple itself at 15 % p.a.?
Solution:
Let P = x, then A = 3x
So, I = A – P
= 3x – x = 2x
We know that S.I = (P × R × T)/100
2x = (x × 15 × T)/100
T = (2x × 100)/(x × 15) = 40/3 = 13.3 years
Example 5. At what per cent will ₹ 1500 amount to ₹ 2400 in 4 years?
P = ₹ 1500
R = ?
T= 4 years and
A = ₹ 2400
S.I. = A – P
= ₹ (2400 – 1500 )
= ₹ 900
S.I. = (P × R × T)/100
900 = (1500 × R × 4)/100
Therefore, R = (900 × 100)/(4 × 1500) = 15%
What is Compound Interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. In compound interest, the principal amount changes w.r.t. to Interest
Some Important Terms:-
Principal: An amount of money that you lend to somebody or invest to earn interest. It is usually denoted by the letter ‘ p ‘
Interest: The extra money that you receive when you invest money or payback when you borrow money. It is usually denoted by SI or CI depending upon the calculation. it is the difference of the Amount and Principal ( A – P )
Time / Period: Time or period for which is borrowed or invested it is usually denoted by ‘t‘
Rate of interest: Rate at which interest is calculated on the principal. It is a percentage value calculated as % per/ annum, denoted by ‘r‘
Amount: Principal + Interest (for a given period at a given rate of interest) this is usually denoted by ‘ A ‘
Quick List of Formulae ( Compound Interest )
If Compounded Yearly
- A = Final Amount Received
- P = Principal
- R= Rate of Interest in % p.a
- t = Time in Years
- C.I = A – P
- A = Final Amount Received
- P = Principal
- R= Rate of Interest in % p.a
- t = Time in Years
- C.I = A – P
- n= number of compounding per year
On Compound Interest a certain sum P, if becomes N times in T years then it becomes N² times in 2T years
N³ times in 3T years
| % Rates | 2 Years | 3 Years |
|---|---|---|
| 5 % | (441/400) × P | ( 9261/8000 ) × P |
| 10 % | 1.21 × P | 1.331 × P |
| 20 % | (36/25) × P | ( 216/125) × P |
| 25 % | ( 25/26 ) × P | ( 125/ 64) × P |
Questions Based On Compound Interest
Example 1: What is the interest recived at the end of 3 years if ₹30,000 is compounded annualy at 10% per annum ?
Solution: Here our Principal = ₹30,000
Rate of Interest = 10% per annum
Time = 3 years
as we know 
in this case 
further simplified to 
= 39,930 = Total Amount. Compound Interest Acquired = ₹39930 – ₹30000 = ₹9930 So our required answer is ₹9930
Method 2: Using the table given above we can just multiply 1.331 to the principal to get the final amount, later we can subtract and get the interest aquired.
30,000 x 1.331 = 39930 => 39930-30000 = 9930 Which is our required answer.
Relation Between CI & SI
Difference Between CI & SI for 2 Years
Difference In Amount:
Difference in %Rate Interest:
Difference Between CI & SI for 3 Years
Difference In Amount:
Principal : ( If difference between CI & SI is given for 3 Years)
