Difference Between Simple Interest and Compound Interest

In this article we are going to be about simple interest and compound interest. It covers the important topics like simple interest and compound interest and simple interest vs compound interest.


What is Simple Interest and Compound Interest?

Simple Interest:

  • In Mathematics, simple interest is a quick and easy method of calculating the interest charge on a given amount of money or loan. 

  • We can determine this by simple interest multiplying the daily rate of interest by the principal by the number of days (n) that elapse between payments.

  • The formula for simple interest is ,

Simple Interest (SI) = (P×R×T)/100


Where, P is equal to the Principal, R is the equal to the Rate of Interest,  T = Time (Period).


The time is in years and the rate of interest is in percentage (%). 


NOTE : 

  • Simple interest is calculated by multiplying the rate of interest by the principal and by the number of days (time period)  that  elapse between  the payments.

  • It benefits consumers who pay their loans on time or early every month.

  • Auto loans and short-term personal loans are examples of places where simple interest is used.

  • We can calculate the total amount,  using the following formula:

Amount = Principal  + Interest 


Where, Amount (A) is equal to the total money paid back at the end of the time period (T)    for which the money was borrowed.


Compound interest:

  • Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period of time.

  • Compound interest is different from the simple interest. 

  • In simple interest the interest is not added to the principal while calculating the interest during the next period while in compound interest the interest is added to the principal to calculate the interest.

  • The formula for compound interest is ,

Compound Interest (CI) = Principal (1+Rate/100)n - principal


where, P is equal to principal ,  R is equal to rate of Interest,  T is equal to Time (Period)


The Formula to Calculate the Amount is


Amount=Principal (1+Rate/100)n


where , P is equal to Principal ,  Rate is equal to Rate of Interest,  n is equal to the time (Period).


Applications of Compound Interest:

Some of the applications of compound interest are:

  1. Increase in population or decrease in population.

  2. Growth of bacteria.

  3. Rise in the value of an item.

  4. Depreciation in the value of an item.


What is the Difference Between Simple Interest and Compound Interest?

  • Besides, simple interest there is another type of interest known as compound interest.

  • The major difference between compound and simple interest is that simple interest is based on the principal of a deposit or a loan whereas compound interest is based on the principal and interest that accumulates in every period of time. 

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Here’s the Difference Between Simple Interest and Compound Interest in a Tabular Form(SI vs CI)


Simple Interest 

Compound Interest

The simple interest is the same for all the number of years.

The compound interest is different for all the years.

SI < CI.

CI > SI.

Simple Interest (SI) = (P×R×T)/100

CI = Principal (1+Rate/100)n - principal


Relation Between Simple Interest and Compound Interest -

Here’s the relation between simple interest and compound interest:

We already know from the SI vs CI definition that the interest is typically expressed as a percentage, and can be simple or compound interest. Simple interest is generally based on the principal amount of a loan or deposit whereas compound interest is based on the principal amount and also on the interest that accumulates on the principal every period. We have already discussed this in the SI vs CI definition.


Questions to be solved:

Question 1) Sohan takes a loan of Rs 1000 from Central bank for a period of one year. The given rate of interest is 10% per annum. Find the interest and the amount Sohan has to pay at the end of one year.

Solution) Let’s write down the given information,

Here, the loan amount = Principal = Rs 1000

Rate of interest = R = 10%

Time for which it is borrowed = T = 1 year

The formula to calculate the simple interest for one year,

Simple Interest (SI) = (P×R×T)/100


Thus, the simple interest for a year, SI = (P × R ×T) / 100 = (1000 × 10 × 1) / 100 = Rs 100

Now, let’s calculate the amount of money at the end of one year,

Amount = Principal  + Interest

The amount that Sohan has to pay to the bank at the end of one  year = Principal + Interest = 1000 + 100 = Rs 1100.


Question 2) Ram borrowed a sum of Rs 5000 for 2 years at the rate of 3% per annum. Find the interest accumulated on the sum of at the end of 2 years and calculate the total amount.

Solution) Let’s write down the given information,

P = Rs 5000

R = 3%

T = 2 years

The formula to calculate the simple interest for one year,

Simple Interest (SI) = (P×R×T)/100


SI = (P × R ×T) / 100 = (5000 ×3 × 2) / 100 = Rs 300

Now, let’s calculate the amount of money at the end of two years,

Amount = Principal + Interest

The amount that Ram has to pay to the bank at the end of two years = Principal + Interest = 5000 + 300 = Rs 5300.


Question 3) Mahi pays Rs 5000 as an amount on the sum of Rs 2000 which he had borrowed for 3 years. What is the rate of interest?

Solution) Let’s write down the given information,

Amount at the end of three years = Rs 5000

Principal= Rs 2000

SI = Amount – Principal = 5000 – 2000 = Rs 3000

Time = 3 years

Rate =?

We know the formula to calculate the simple interest,

SI = (P × R ×T) / 100 

R = (Simple Interest × 100) /(Principal× Time)

R = (3000 × 100 /5000 × 3) =0.2% 

Thus, R = 0.2%


Question 4) The count of a certain breed of bacteria was found to increase at the rate of 5% per hour. What will be the growth of  bacteria at the end of 3 hours if the count was initially 6000.

Solution:

Since the population of bacteria increases at the rate of 5% per hour,

We know the formula for calculating the amount,

Amount= Principal(1 + R/100)n

Thus, the population at the end of 3 hours = 6000(1 + 3/100)3

= 6000(1 + 0.03)3 = 6000(1.03)3 =  Rs 6556.36.

FAQ (Frequently Asked Questions)

Question 1) What is the Main Difference Between Simple and Compound Interest and How do you Calculate Simple Interest and Compound Interest?

Answer) The concept of simple interest is based on the principal amount of a loan or deposit, while the concept of compound interest is mainly based on the principal amount and the interest that accumulates on it in every period (time ).It is easier to calculate simple interest than compound interest since simple interest is calculated only on the principal amount of a loan or deposit.The formula for simple interest is Interest = Principal x Rate x Time. To compute compound interest we use the formula: Amount = P*(1 + r/100)t.