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**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**

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.

**Time**

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**

**P**=(100×SI)/ RT

**R**=(100×SI)/ PT

**T**=(100×SI)/ PR

**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?**

Solution:

Amount for 2 years(A_{2}) = 702

Amount for 3 years (A_{3})= 783

Interest for 1 year (I) = 783-702 = 81

So Sum = A_{2} – 2I = 702 – 2×81

= 702-162 = 540

rate of interest = (81/540)×100

= 15%

Amount after 5 years = Sum+5I

= 540+ 5×81

= 945

**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%

**Apply allegation:**

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