Published by: **Divyanshu Nay****ak**

## 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

**, denoted by ‘**

*% per/ annum**‘*

**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 )**

**Quick List of Formulae**

**( Simple Interest )**

**SI**= (x**P**x*R*) /*T***100****P**= Principal**R**= Rate of Interest % p.a**T**= Time Interval

x*P = ( 100*x*SI ) / ( R*)*T*x*R = ( 100*x*SI ) / ( P*)*T*x*T = ( 100*x*SI ) / ( P*)*R***Amount**==*P + SI***A****Interest Acquired**== (*A – P**PRT) / 100*- If a sum becomes
times in*N*years, then*t***RT = 100 ( N – 1 )**- OR
*R = ( N – 1 ) / T × 100 %*

- OR

If ** R = T **then,

**Let’s Solve Some Examples**:-

**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 = 40

*/ 100 = 2*

**x****/ 5**

*x***A = P + I**

A =

**+ 2**

*x***/5**

*x*A = (5

**+ 2**

*x***)/5 = 7**

*x***/5 [**

*x***But given that A = ₹ 2520**]

7

**/5 = 2520**

*x*7

*= 2520 × 5*

**x****= (2520 × 5) / 7 =**

*x***₹ 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 = 2

*x*Also,

**S.I = A – P**

= 2

**–**

*x*

*x*=

*x*Therefore:-

*S.I = P*T = 6 years

We know that

**S.I. = (P × R × T) / 100**

(

**× R × 6)/100 =**

*x*

*x*R = 100

**/6**

*x***=**

*x***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 = 3*x*

So, **I = A – P**

= 3** x** –

**= 2**

*x*

*x*We know that

**S.I = (P × R × T)/100**

2

**= (**

*x***× 15 × T)/100**

*x*T = (2

**× 100)/(**

*x***× 15) = 40/3 =**

*x***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

**, denoted by ‘**

*% per/ annum**‘*

**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

= Final Amount Received*A*= Principal*P*= Rate of Interest in % p.a*R*= Time in Years*t**C.I = A – P*

= Final Amount Received*A*= Principal*P*= Rate of Interest in % p.a*R*= Time in Years*t**C.I = A – P*= number of compounding per year*n*

On Compound Interest a certain sum ** P**, if becomes

**times in**

*N***years then it becomes**

*T***times in**

*N²***years**

*2T***times in**

*N³***years**

*3T* % 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 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)