Compound interest eases the calculations. Compound interest is based on the principal amount and the interest that will accumulate in every period.

Formula for finding amount:

A = P ( 1 + r/100 ) ^T. Here, the symbol “^” stands for as a symbol for the concept of: “power of” or “raise to“.

Where,

A = Amount 

P = Principal Amount

R = Rate of Interest

T = Time Period

Formula for finding Compound Interest: 

Compund Interest = Amount - Principal 

Where compound interest is used?

Compound interest (CT) is mostly used for transactions in the banking sector, financial sectors, or other areas. Compound interest real-life instances are a raptopicId increase in the number of cases owing to a disease like plague or covtopicId.

Compound interest rates can be expressed in different interest rates like compounded yearly, compounded half-yearly, compounded quarterly, monthly,  daily, etc

Compound interest formula for half yearly: 

A = P( 1+ r/2*100)^ 2*t

Compound interest formula for quarterly:

A= P( 1+ r/4*100)^4*t

Problem sum: 

Shobhita took a loan of ₹ 35000 at a compound interest of 6% for two years. Determine the total amount due to the bank at the conclusion of the two-year period.

Solution: Principal = ₹ 35000

Rate of interest = 6% 

Time = 2 years

Amount =  P * ( 1+ r/100) ^t

             = 35000 * ( 1 + 6/100 ) ^ 2 

             = 35000 * ( 1.06 ) ^2

             = ₹  39326

CI = Amount - Principal 

     = ₹ 39326 - ₹35000

     = ₹4326

Therefore, Shobhita has to pay Rs.39,326 to the bank at the end of two years.

Problem sum: 

Meenakshi borrowed Rs.1,00,00 for three years at the rate of 5% per annum. Find the difference between simple interest and compound interest. 

Solution: Let us start by assuming that Meenakshi has borrowed money based on simple interest.

Principal = Rs 1,00,000

Rate of int= 5% 

Time = 3 years 

SI = P*R*T /100

    = (100000 * 5 * 3)/ 100

    =₹ 15000

So, the simple interest will be rupees 15,000. 

Let us start by assuming that Meenakshi has borrowed money based on compound interest

Amount = P * ( 1+ r/ 100 ) ^T 

             = 100000 * ( 1 + 5/100) ^3

             = 100000 * ( 1.05 )^3

             = 115762.5 

CI = Amount - Principal 

     = 115762.5   -  100000

     = ₹ 15762.5 

So, the compound interest is Rs.15,762.5 

Hence, the simple interest and compound interest difference is given by:

CI - SI= 15762.5 - 15000

          =  ₹ 762.5

Hence, if Meenakshi chose compound interest then she has to pay Rs.762.5 more than that of simple interest.

FAQS:

Can interest be calculated by both simple and compound interests?

Solution: Yes, interest can be calculated either by compound interest or by simple interest. But, they are different.

What is the key distinction that differentiates simple from compound interest?

Solution: The key distinction between compound interest and simple interest is the amount received at the end. That is, simple interest is calculated on the deposited amount from borrowed money or principal amount. On the other hand, compound interest is calculated on principal money and includes the interest that is compounded over a duration of time. Compound and simple interest are computed utilizing entirely different formulas.

Which is simple to calculate - simple or compound interest?

Solution: When compared to compound interest, simple interest is easier to calculate.

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