# Quantitative Aptitude : Simple Interest and Compound Interest

Simple Interest and Compound Interest are some of the most important topics in SSC CGL exam as they have practical application in banking too. If you face confusion in understanding SI and CI, Then this article will provide will clear concept of the two.

### What is Interest?

Interest is the amount paid to the loaner (who loans something) or gained on the amount called principal amount that we have borrowed or lent.

It is charged according to a rate called interest rate and usually charged annually. There are two types of interests:-

1.Simple Interest

2. Compound Interest

**Simple Interest**

**Definition:- **In simple interest (SI) the interest rate is calculated on the initial loaned amount also called as principal amount.

Let you borrowed 1000 rupees at 10% rate.

Interest for the 1st year = 10% of 1000

= (10/100) x 1000

= (100~~00~~/1~~00~~)

= 100

so interest after 1st year is Rs. 100

total amount=1000 +100=1100

For 2nd year Total amount=1100

interest after 2nd year = ~~10% of 1100~~

No, I already told that in definition the interest is always calculated on the principal amount only

so Interset after 2nd year = 10% of 1000

= (10/100) x 1000

= (100~~00~~/1~~00~~)

= 100

So, we can see interest amount is constant for every year. It can be calculated by following formula

Here, P = Principal / amount invested/amount borrowed.

R = Rate of interest per annum.

T =time in years.

& the final Amount = Principal + Simple interest

**Note:** If the rate of interest is not given in per annum then change the time according to the period over which interest is given.

For example: If interest is given as 10 % per quarter for 3years on Rs.5000, then the time will have to be changed into quarters.

Time = 3 years = 3× 4 = 12 quarters

SI = ( 5000x10x12 )/100

= 6000

So, interest amount is Rs. 6000.

**Compound Interest**

In compound interest method, interest for each period is added to the principal before interest is calculated for the next period. It means that the amount of interest is calculated on the total amount after the end of each interest period.

e.g.

Q. A bank offers 5% compound interest calculated on the half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1^{st} July of a year. At the end of the year, the amount he would have gained by way of interest is:

Sol.

The formula is given by;-

When compound interest Compounded half-yearly, then R% become and time T becomes 2T. For quarterly compounding, we can change the rate and time accordingly.

Some Example problems are below:-

**Problem 1.** A sum of Rs. 25000 becomes Rs. 27250 at the end of 3 years when calculated at simple interest. Find the rate of interest.

__Solution__:

Simple interest = 27250 – 25000 = 2250

Time = 3 years.

SI = PTR / 100 → R = SI * 100 / PT

R = 2250 * 100 / 25000 * 3 → R = 3%.

**Problem 2.** Find the present worth of Rs. 78000 due in 4 years at 5% interest per year.

__Solution__:

The amount with interest after 4 years = Rs. 78000

Therefore, simple interest = 78000 – Principal.

Let the principal amount be p.

78000 – p = p*4*5/100 → p=13000

Principal = 78000 – 13000 = Rs. 65000

**Problem 3.** A certain principal amounts to Rs. 15000 in 2.5 years and to Rs. 16500 in 4 years at the same rate of interest. Find the rate of interest.

__Solution__:

Amount becomes 15000 in 2.5 years and 16500 in 4 years.

Simple interest for (4-2.5) years = 16500 – 15000

Therefore, SI for 1.5 years = Rs. 1500.

SI for 2.5 years = 1500/1.5 * 2.5 = 2500

Principal amount = 15000 – 2500 = Rs. 12500.

Rate of Interest = 2500 * 100 / 12500 * 2.5 → R = 8%.

**Problem 4.** Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.

__Solution__:

Amount with CI = 3000 (1+ 5/100)^{2} = Rs. 3307.5

Therefore, CI = 3307.5 – 3000 = Rs. 307.

Here are some questions for your practice.

**Problem 5. **A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.

**Problem 6.** The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal.

**Problem 7.** Find the simple interest on Rs. 5000 at a certain rate if the compound interest on the same amount for 2 years is Rs. 253.125.

**Problem 8.** A certain amount becomes Rs. 5760 in 2 years and Rs. 6912 in 3 years. What is the principal amount and the rate of interest?

**Problem 9.** How long will it take a certain amount to increase by 30% at the rate of 15% simple interest?

**Answers**

5. 3.5years

6. 2000

7.250

8. 20% and 4000

9. 2years