Simple and Compound Interest:

Interest is the fixed amount paid on borrowed money.

The sum lent is called the principal. The sum of the principal and interest is called the Amount.

Interest is of two kinds:

- Simple interest is calculated on the principal, or original, amount of a loan.

- Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as  " Interest on Interest "

Example on Simple Interest

Suppose you deposit 100rs to the Bank on SI at rate of 10% for 3 years.

100  -----10%----- => 10(interest)

100- -----10%----- => 10(interest)

100------10%----- => 10(interest)

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Total 30rs interest bank will give you after 3years.

Simple interest is always calculated on principal.

Example of Compound Interest

Suppose you deposit 100rs to the Bank on CI at rate of 10% for 3 years.

100 ------10%-----=> 10  ---- Now Amount= 100+10 = 110

110------10%------=> 11 --- Now Amount= 110+11= 121

121------10%------=> 12.1  Now Amount = 121 +12.1 =133.1

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Total 33.1rs Interest bank will give you after 3years.

Compound interest is always calculated on Amount.

Simple Interest Formula:

SI =  (P * R * T ) /100

Compound Interest Formula:   CI =  P ( 1+ r/100)ⁿ  - P

Amount = Compound interest + Prinicipal

CI = A – P    =  A = ( 1+ r/100)ⁿ

Now , In the Questions it might have told , Mr X invested an amount/Sum/money

Any kind of Investment   -- That means Principal

Now What is Amount : Suppose u invest 1000rs and you get an interest of 100rs , then at the end of 1 year you get : P(1000) + I(100)  = A(1100)

So Amount will be always       Amount = Principal +  SI/CI

Binomial Theorem Formula for Calculating simple and Compound Interest

Compound Interest for 2 years:  2a+ b

Where a = p * r /100

              b = a * r/100

Compound Interest for 3 years :  3a + 3b + c

Where a = p * r /100

              b = a * r/100

              c = b * r/100

(CI) – (SI) for 2years = ( p *r²) / 100²          (Compound and Simple interest difference for 2 years)

(CI) – (SI) for 3years = p *r² (300+r) / 100³  (Compound and Simple Interest difference for 3 years)

At what rate of simple interest per annum will a sum of Rs. 7200 amounts to Rs. 9000 in 5 years?

a) 5% p. a.                    b) 8% p. a.                    c) 4% p. a.                    d) 6% p. a.

Solution:

Given that, P = Rs. 7200, T = 5 years, and Amount A = Rs. 9000

SI = A – P = 9000 – 7200 = Rs. 1800                             ⸪ A = P + SI

Rate of interest R = (100 × SI) / PT = (100 × 1800) / (7200 × 5) = 5% p.a.

Answer: a

Anurag invested an amount of Rs. 58000 at a rate of 15% p.a. compound interest for a period of 2 years. What amount will he get at the end of 2 years, if the interest is compounded annually?

a) Rs. 72450                  b) Rs. 76705                 c) Rs. 71245                  d) Rs. 72405

Solution:

Given that, P = Rs. 58000, R = 15% p.a. and T = 2 years

Final amount A = P (1 + R/100)^T = 58000 (1 + 15/100)²  

⸫ Final amount A = 58000 × (115 / 100) × (115 / 100) = Rs. 76705.

Answer: b

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