# Simple Interest and Compound Interest – Concepts and Formula

## Simple Interest and Compound Interest

One of the most prevalent quantitative aptitude topics asked in government tests is Simple Interest and Compound Interest. This is one of those topics that students are already aware of before they begin studying for competitive exams.

Although the concepts of Simple Interest and Compound Interest remain the same, the kind of questions presented in exams may vary.

2-3 word problems related to Simple Interest and Compound Interest are asked in exams, but candidates may also expect questions about data sufficiency and data interpretation related to Simple Interest and Compound Interest.

So, we are providing you with concepts and formulas of the Simple Interest and Compound Interest

### Simple Interest

Simple interest is calculated by multiplying the interest rate by the principal amount and the time period which is generally in years. The S.I. formula is given as:

### Formula for Simple Interest

S.I = simple interest

R = rate of interest

T = time

### Compound Interest

Compound interest is an interest accumulated on the principal and interest together over a given time period.

The interest accumulated on a principal over a period of time is also accounted under the principal. Further, the interest calculation for the next time period is on the accumulated principal value.

A sum of money of Rs 100 invested over a period of time for a 10% rate would give a simple interest of Rs10, Rs10, Rs10… over successive time periods of 1 year, but would give a compound interest of  Rs10, Rs11, Rs12.1, Rs13.31… Let us understand more about this, and the calculations of compound interest in the below content.

### Formula for Compound Interest

Where,
P = Principal
r = rate of interest
t = time
Amount = Principal + compound interest

Example 1. Vandana takes a loan of Rs 10000 from a bank for a period of 1 year. The rate of interest is 10% per annum. Find the interest and the amount he has to pay at the end of a year.

Solution

Here, the loan sum = P = Rs 10000
Rate of interest per year = R = 10%
Time for which it is borrowed = T = 1 year
Thus, simple interest for a year,
SI = (P × R ×T) / 100 = (10000 × 10 ×1) / 100 = Rs 1000

Amount that Vandana has to pay to the bank at the end of the year
= Principal + Interest
= 10000 + 1000 = Rs 11,000

Example 2 Mamta borrowed Rs 40,000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years.

Solution:

P = Rs 40,000
R = 3.5%

T = 3 years

SI = (P × R ×T) / 100 = (40,000× 3.5 ×3) / 100 = Rs 4200

Example 3: Pankaj pays Rs 7500 as an amount on the sum of Rs 6000 that he had borrowed for 2 years. Find the rate of interest.

Solution:

A = Rs 7500
P = Rs 6000
SI = A – P = 7500 – 6000 = Rs 1500
T = 2 years
R = ?

SI = (P × R ×T) / 100

R = (SI  × 100) /(P× T)

R = (1500  × 100 /6000 × 2)  =12.5 %

Thus,  R  = 12.5%

Example 4 What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?

Solution

Amount = 35123.20
Compound Interest = 35123.20 – 25000 = 10123.20

### Difference between S.I and C.I for 2 Years

Example 5: The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is ?

Solutions

Using Formula

25 = P (10/100)2
P = 2500,

The sum will be 2500

### Difference between S.I and C.I for 3 Years

Example 6 : The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is ?

Solutions

Using formula

372 = P (10/100)2{(300+10)/100}
37200 = P(310/100)
P = 37200×100/310 = 12000

Or Another way

Let us assume

P= Rs. 1000. SI= Rs. 300, CI = Rs. 331
Difference = 331 – 300 = Rs. 31.
Applying the unitary method,
the difference Rs. 372 is 12 times Rs. 31.
Therefore, the principle will also be 12 times of Rs. 1000 i.e. Rs. 12000.

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