Question

Find out the difference between compound interest and simple interest if P = 20,000, R = 10.5
p.c.p.a and N = 2 years . ​

Answer 1

Answer:

Difference 220.5

Step-by-step explanation:

Given,

P= 20,000 R= 10.5 p.c.p.a and T= 2 years,

SI for 2 years

(10.5*2)%of 20000=2200

CI for 2 years

12.1025% of 20000=2420.5         (CI for 2 years formula 2R+(R^2/100))

So,

Difference is 2420.5-2200=220.5

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Answer 2

Given :-

Principal = ₹20,000

Time = 2 years

Rate = 10.5%

To find :-

Difference between Compound interest and Simple Interest

Simple interest :-

$Simple\: interest= \dfrac{Principal\times Rate\times Time}{100}$

substituting the values,

$si = \dfrac{20,000\times2\times10.5}{100}$

$si = \dfrac{20,000\times21}{100}$

$si = \dfrac{200\not0\not0\times21}{1\not0\not0}$

$si = 200\times21$

SIMPLE INTEREST = ₹4200

Compound Interest :-

$Amount = Principal\bigg(1+\dfrac{rate}{100}\bigg)^{time}$

Compound interest = Amount - Principal

Substituting the values,

$a = 20,000\bigg(1+\dfrac{10.5}{100}\bigg)^{2}$

$a = 20,000\bigg(1+\dfrac{10.5\times10}{100\times10}\bigg)^{2}$

$a = 20,000\bigg(1+\dfrac{105}{1000}\bigg)^{2}$

$a = 20,000\bigg(\dfrac{1000+105}{1000}\bigg)^{2}$

$a = 20,000\bigg(\dfrac{1105}{1000}\bigg)^{2}$

$a = 20,000\bigg(\dfrac{221}{200}\bigg)^{2}$

$a =20,000\times \dfrac{221}{200} \times \dfrac{221}{200}$

$a = 2\not0\not0\not0\not0\times\dfrac{221}{2\not0\not0} \times \dfrac{221}{2\not0\not0}$

$a = \not2\times\dfrac{221}{\not2} \times \dfrac{221}{2}$

$a = \dfrac{221\times221}{2}$

$a = \dfrac{48,841}{2}$

$a = 24420.5$

Compound interest = A - P

CI = ₹24420.5 - 20000

CI = ₹4420.5

Difference :-

Compound interest - Simple Interest

=> ₹4420.5 - ₹4200

=> ₹220.5

Some more formulas :-

Compounded half-yearly

$Amount = Principal\bigg(1+\dfrac{rate}{200}\bigg)^{2\times time}$

Compounded quarterly

$Amount = Principal\bigg(1+\dfrac{rate}{400}\bigg)^{4\times time}$