Simple and Compound Interest is an important segment of an Arithmetic section under Quantitative Aptitude.

In this article, we will discuss the concepts of Simple Interest and talk about how to solve and approach the questions based on this topic.

You can also read the basics of Simple Interest from the link given below-

**Basics of Simple Interest**

**Example 2:** If the principal is 100 Rs. Difference of Simple Interest for 4yrs and 6yrs is Rs 8. Calculate the rate of simple interest.

Solution: In simple interest questions, interest always remains same for a year if the principal, rate of interest is constant for the same.

Let Interest for 4 yrs is I then interest for 6 yrs is (I+8)

interest for 2 yrs is Rs. 8

interest for 1 yr = 4

rate of interest = (4/100) × 100 = 4%

**Example3:** If the amount is (10/9) times of Principal and rate of interest and time both are numerically equal. Then, what is the rate of interest per annum?

Solution: Let Principal is P. Given, numerically R = T

Interest = Amount – principal

I = (10/9)P – P

I = P/9 (Interest is in the multiples of Principal)

Now, I =[(P×R×T)/100]

P/9 = (P× R× T)/100

R^{2} = 100/9 (using, R=T)

R = (10/3)%

We can also say the time period is (10/3)years.

**Short approach:** Whenever Interest is in multiple of Principal and Rate of Interest and Time period is equal.

**Annual Instalments for Simple Interest:**

**Let's discuss a real example to understand instalment concepts:**

A person deposit Rs.140 to bank every year up to 5 yrs . The bank gives him 5% rate of interest simple annually. And at the end of 5 yrs he get 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 annual payment. Debt is total amount, so don’t confuse between these two terms.

**Installment =**

**where A = debt, r = rate of interest and t = time period**

**Example4**: 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

**Some Important examples based on Simple Interest.**

**Example5:** 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

**Example6:** 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

**Example7:** 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

**Example8:** 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

And 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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