Question

Paras takes a loan of 20,000 at a compound interest rate of 5% per annum (p.a.)

(i) Find the compound interest after one year.

(ii) Find the compound interest for two years.

(iii) Find the sum of money required to clean the debt at the end of two years.

(iv) Find the difference between the compound interest and the simple interest
same rate for two years.​

Answer 1

$\bf{\underline{Given:-}}$

• Principal = Rs.20000
• Rate = 5%

$\bf{\underline{To\:find:-}}$

(i) The compound interest after one year.

(ii) The compound interest after two years.

(iii) The sum of money required to clean the debt at the end of two years.

(iv) The difference between the compound interest and the simple interest at same rate for two years.

$\bf{\underline{Solutions:-}}$

(i) P = Rs.20000

R = 5%

T = 1 year

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^t}$

= $\sf{A = 20000\bigg(1+\dfrac{5}{100}\bigg)^1}$

= $\sf{A = 20000\bigg(\dfrac{100+5}{100}\bigg)^1}$

= $\sf{A = 20000\bigg(\dfrac{105}{100}\bigg)^1}$

= $\sf{A = 20000\times\dfrac{105}{100}}$

= $\sf{A = 21000}$

$\sf{CI = A - P}$

= $\sf{CI = 21000 - 20000}$

= $\sf{CI = 1000}$

Therefore CI after 1 year will be Rs.1000.

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(ii) P = Rs.20000

R = 5%

T = 2 years

$\sf{A = 20000\bigg(1+\dfrac{5}{100}\bigg)^2}$

= $\sf{A = 20000\bigg(\dfrac{100+5}{100}\bigg)^2}$

= $\sf{A = 20000\bigg(\dfrac{105}{100}\bigg)^2}$

= $\sf{A = 20000\times\dfrac{105}{100}\times\dfrac{105}{100}}$

= $\sf{A = 22050}$

= $\sf{CI = 22050 - 20000}$

= $\sf{CI = Rs.2050}$

Therefore CI after 2 years will be Rs.2050

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(iii) Sum of money at the end of 2 year to clear the debt = (CI after 1 year) + (CI after 2 years)

$\sf{Sum\:of\:money = 2050 + 1000}$

$\sf{Sum\:of\:money = 3050}$

Therefore the sum of money required to clear the debt at the end of 2 years is Rs.3050

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(iv) Difference between SI and CI after two years:-

P = 20000

R = 5%

T = 2 years

$\sf{SI = \dfrac{P\times R\times T}{100}}$

= $\sf{SI =\dfrac{20000\times 5\times 2}{100}}$

= $\sf{SI = Rs.2000}$

CI after 2 years = Rs.2050

Difference between CI and SI

= $\sf{2050-2000}$

= $\sf{50}$

Therefore the difference between CI and SI after 2 years will be 50.

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Answer 2

Step-by-step explanation:

given that -

p = 20000

rate = 5%

question 1-

(i) Find the compound interest after one year.

amount = p ( 1 + r/100)^1

= 20000 ( 1+ 5/100)^1

= 20000( 21/20)

= 20000×21/20

= 21000 rs

now, c.I = a - p = 21000- 20000= 1000 rs